From ebff8c536160341f836f68dfcfb2dc953f3784e1 Mon Sep 17 00:00:00 2001 From: Dimitri Lozeve Date: Wed, 8 Apr 2020 17:40:56 +0200 Subject: [PATCH 1/9] Add post on OR --- _site/archive.html | 4 + _site/atom.xml | 46 ++++++++++ _site/index.html | 4 + .../posts/operations-research-references.html | 92 +++++++++++++++++++ _site/rss.xml | 46 ++++++++++ posts/operations-research-references.org | 44 +++++++++ 6 files changed, 236 insertions(+) create mode 100644 _site/posts/operations-research-references.html create mode 100644 posts/operations-research-references.org diff --git a/_site/archive.html b/_site/archive.html index 370c561..c9b5f6b 100644 --- a/_site/archive.html +++ b/_site/archive.html @@ -51,6 +51,10 @@ ICLR 2020 Notes: Speakers and Workshops - May 5, 2020 +
  • + Operations Research and Optimisation: where to start? - April 8, 2020 +
    • +
  • Reading notes: Hierarchical Optimal Transport for Document Representation - April 5, 2020
    • diff --git a/_site/atom.xml b/_site/atom.xml index f50f860..ef6e778 100644 --- a/_site/atom.xml +++ b/_site/atom.xml @@ -65,6 +65,52 @@ ]]> + + Operations Research and Optimisation: where to start? + + https://www.lozeve.com/posts/operations-research-references.html + 2020-04-08T00:00:00Z + 2020-04-08T00:00:00Z + +
    + +
    +
    +

    Operations research (OR) is a vast area comprising a lot of theory, different branches of mathematics, and too many applications to count. In this post, I will try to explain why I find it so fascinating, but also why it can be a little disconcerting to explore at first. Then I will try to ease the newcomer’s path in this rich area, by suggesting a very rough “map” of the field and a few references to get started.

    +

    Keep in mind that although I studied it during my graduate studies, this is not my primary area of expertise (I’m a data scientist by trade), and I definitely don’t pretend to know everything in OR. This is a field too vast for any single person to understand in its entirety, and I talk mostly from a “amateur mathematician and computer scientist” standpoint.

    +

    Why is it hard to approach?

    +
      +
    • why it may be more difficult to approach than other, more recent areas like ML and DL +
        +
      • slightly longer history
        • +
      • always very close to applications: somehow more “messy” in its notations, vocabulary, standard references, etc, as other “purer” fields of maths (similar to stats in this regard)
        • +
      • often approached from a applied point of view means that many very different concepts are often mixed together
        • +
      • +
    • why it is interesting and you should pursue it anyway +
        +
      • history of the field
        • +
      • examples of applications
        • +
      • theory perspective, rigorous field
        • +
      • +
    • different subfields +
        +
      • optimisation: constrained and unconstrained
        • +
      • game theory
        • +
      • dynamic programming
        • +
      • stochastic processes
        • +
      • simulation
        • +
      • +
    • how to learn and practice +
        +
      • references
        • +
      • courses
        • +
      • computational assets
        • +
      • +
    +
    + +]]>     +     Reading notes: Hierarchical Optimal Transport for Document Representation diff --git a/_site/index.html b/_site/index.html index 299d0eb..2a7c926 100644 --- a/_site/index.html +++ b/_site/index.html @@ -74,6 +74,10 @@ public key: RWQ6uexORp8f7USHA7nX9lFfltaCA9x6aBV06MvgiGjUt6BVf6McyD26 ICLR 2020 Notes: Speakers and Workshops - May 5, 2020 +
  • + Operations Research and Optimisation: where to start? - April 8, 2020 +
    • +
  • Reading notes: Hierarchical Optimal Transport for Document Representation - April 5, 2020
    • diff --git a/_site/posts/operations-research-references.html b/_site/posts/operations-research-references.html new file mode 100644 index 0000000..c522320 --- /dev/null +++ b/_site/posts/operations-research-references.html @@ -0,0 +1,92 @@ + + + + + + + + + Dimitri Lozeve - Operations Research and Optimisation: where to start? + + + + + + + + + + + + + + + + +
    + +
    + + +

    Operations Research and Optimisation: where to start?

    + + +

    April 8, 2020

    + +
    + + + +
    + +
    +
    + +
    +
    +

    Operations research (OR) is a vast area comprising a lot of theory, different branches of mathematics, and too many applications to count. In this post, I will try to explain why I find it so fascinating, but also why it can be a little disconcerting to explore at first. Then I will try to ease the newcomer’s path in this rich area, by suggesting a very rough “map” of the field and a few references to get started.

    +

    Keep in mind that although I studied it during my graduate studies, this is not my primary area of expertise (I’m a data scientist by trade), and I definitely don’t pretend to know everything in OR. This is a field too vast for any single person to understand in its entirety, and I talk mostly from a “amateur mathematician and computer scientist” standpoint.

    +

    Why is it hard to approach?

    +
      +
    • why it may be more difficult to approach than other, more recent areas like ML and DL +
        +
      • slightly longer history
        • +
      • always very close to applications: somehow more “messy” in its notations, vocabulary, standard references, etc, as other “purer” fields of maths (similar to stats in this regard)
        • +
      • often approached from a applied point of view means that many very different concepts are often mixed together
        • +
      • +
    • why it is interesting and you should pursue it anyway +
        +
      • history of the field
        • +
      • examples of applications
        • +
      • theory perspective, rigorous field
        • +
      • +
    • different subfields +
        +
      • optimisation: constrained and unconstrained
        • +
      • game theory
        • +
      • dynamic programming
        • +
      • stochastic processes
        • +
      • simulation
        • +
      • +
    • how to learn and practice +
        +
      • references
        • +
      • courses
        • +
      • computational assets
        • +
      • +
    +
    +
    + + +
    + Site proudly generated by + Hakyll +
    + + diff --git a/_site/rss.xml b/_site/rss.xml index 68ec24f..315b9c7 100644 --- a/_site/rss.xml +++ b/_site/rss.xml @@ -64,6 +64,52 @@ https://www.lozeve.com/posts/iclr-2020-notes.html Dimitri Lozeve + + Operations Research and Optimisation: where to start? + https://www.lozeve.com/posts/operations-research-references.html + +
    + +
    +
    +

    Operations research (OR) is a vast area comprising a lot of theory, different branches of mathematics, and too many applications to count. In this post, I will try to explain why I find it so fascinating, but also why it can be a little disconcerting to explore at first. Then I will try to ease the newcomer’s path in this rich area, by suggesting a very rough “map” of the field and a few references to get started.

    +

    Keep in mind that although I studied it during my graduate studies, this is not my primary area of expertise (I’m a data scientist by trade), and I definitely don’t pretend to know everything in OR. This is a field too vast for any single person to understand in its entirety, and I talk mostly from a “amateur mathematician and computer scientist” standpoint.

    +

    Why is it hard to approach?

    +
      +
    • why it may be more difficult to approach than other, more recent areas like ML and DL +
        +
      • slightly longer history
        • +
      • always very close to applications: somehow more “messy” in its notations, vocabulary, standard references, etc, as other “purer” fields of maths (similar to stats in this regard)
        • +
      • often approached from a applied point of view means that many very different concepts are often mixed together
        • +
      • +
    • why it is interesting and you should pursue it anyway +
        +
      • history of the field
        • +
      • examples of applications
        • +
      • theory perspective, rigorous field
        • +
      • +
    • different subfields +
        +
      • optimisation: constrained and unconstrained
        • +
      • game theory
        • +
      • dynamic programming
        • +
      • stochastic processes
        • +
      • simulation
        • +
      • +
    • how to learn and practice +
        +
      • references
        • +
      • courses
        • +
      • computational assets
        • +
      • +
    +
    + +]]>     + Wed, 08 Apr 2020 00:00:00 UT + https://www.lozeve.com/posts/operations-research-references.html + Dimitri Lozeve +     Reading notes: Hierarchical Optimal Transport for Document Representation https://www.lozeve.com/posts/hierarchical-optimal-transport-for-document-classification.html diff --git a/posts/operations-research-references.org b/posts/operations-research-references.org new file mode 100644 index 0000000..1900610 --- /dev/null +++ b/posts/operations-research-references.org @@ -0,0 +1,44 @@ +--- +title: "Operations Research and Optimisation: where to start?" +date: 2020-04-08 +--- + +[[https://en.wikipedia.org/wiki/Operations_research][Operations research]] (OR) is a vast area comprising a lot of theory, +different branches of mathematics, and too many applications to +count. In this post, I will try to explain why I find it so +fascinating, but also why it can be a little disconcerting to explore +at first. Then I will try to ease the newcomer's path in this rich +area, by suggesting a very rough "map" of the field and a few +references to get started. + +Keep in mind that although I studied it during my graduate studies, +this is not my primary area of expertise (I'm a data scientist by +trade), and I definitely don't pretend to know everything in OR. This +is a field too vast for any single person to understand in its +entirety, and I talk mostly from a "amateur mathematician and computer +scientist" standpoint. + +* Why is it hard to approach? + +- why it may be more difficult to approach than other, more recent + areas like ML and DL + - slightly longer history + - always very close to applications: somehow more "messy" in its + notations, vocabulary, standard references, etc, as other "purer" + fields of maths (similar to stats in this regard) + - often approached from a applied point of view means that many very + different concepts are often mixed together +- why it is interesting and you should pursue it anyway + - history of the field + - examples of applications + - theory perspective, rigorous field +- different subfields + - optimisation: constrained and unconstrained + - game theory + - dynamic programming + - stochastic processes + - simulation +- how to learn and practice + - references + - courses + - computational assets From 9e234846698234198a5f29c03055acb91d70ede5 Mon Sep 17 00:00:00 2001 From: Dimitri Lozeve Date: Fri, 10 Apr 2020 18:18:16 +0200 Subject: [PATCH 2/9] Update post --- posts/operations-research-references.org | 16 ++++++++++++++++ 1 file changed, 16 insertions(+) diff --git a/posts/operations-research-references.org b/posts/operations-research-references.org index 1900610..96cb972 100644 --- a/posts/operations-research-references.org +++ b/posts/operations-research-references.org @@ -20,6 +20,22 @@ scientist" standpoint. * Why is it hard to approach? +Operations research can be difficult to approach, since there are many +references and subfields. Compared to machine learning for instance, +OR has a slightly longer history (going back to the 17th century, for +example with Monge and the optimal transport problem). This means that +good textbooks and such have existed for a long time, but also that +there will be plenty of material to choose from. + +Moreover, OR is very close to applications. Sometimes methods may vary +a lot in their presentation depending on whether they're applied to +train tracks, sudoku, or travelling salesmen. In practice, the +terminology and notations are not the same everywhere. This is +disconcerting if you are used to mathematics, where notations evolved +over a long time and is pretty much standardised for many areas. In +contrast, if you're used to the statistics literature with its [[https://lingpipe-blog.com/2009/10/13/whats-wrong-with-probability-notation/][strange +notations]], you will find that OR is actually very well formalised. + - why it may be more difficult to approach than other, more recent areas like ML and DL - slightly longer history From abb6bd0b901a7c650eea7df93d0869b0c8d2a416 Mon Sep 17 00:00:00 2001 From: Dimitri Lozeve Date: Tue, 26 May 2020 16:17:24 +0200 Subject: [PATCH 3/9] Update post --- _site/archive.html | 4 +- _site/atom.xml | 109 ++++++++++-------- _site/index.html | 4 +- .../posts/operations-research-references.html | 17 ++- _site/rss.xml | 109 ++++++++++-------- bib/bibliography.bib | 8 ++ posts/operations-research-references.org | 53 +++++++-- 7 files changed, 197 insertions(+), 107 deletions(-) diff --git a/_site/archive.html b/_site/archive.html index c9b5f6b..99dc5fb 100644 --- a/_site/archive.html +++ b/_site/archive.html @@ -48,11 +48,11 @@
    • - ICLR 2020 Notes: Speakers and Workshops - May 5, 2020 + Operations Research and Optimisation: where to start? - May 26, 2020
    • - Operations Research and Optimisation: where to start? - April 8, 2020 + ICLR 2020 Notes: Speakers and Workshops - May 5, 2020
    • diff --git a/_site/atom.xml b/_site/atom.xml index ef6e778..9d2970c 100644 --- a/_site/atom.xml +++ b/_site/atom.xml @@ -8,8 +8,69 @@ Dimitri Lozeve dimitri+web@lozeve.com - 2020-05-05T00:00:00Z + 2020-05-26T00:00:00Z + Operations Research and Optimisation: where to start? + + https://www.lozeve.com/posts/operations-research-references.html + 2020-05-26T00:00:00Z + 2020-05-26T00:00:00Z + +
      + +
      +
      +

      Operations research (OR) is a vast area comprising a lot of theory, different branches of mathematics, and too many applications to count. In this post, I will try to explain why I find it so fascinating, but also why it can be a little disconcerting to explore at first. Then I will try to ease the newcomer’s path in this rich area, by suggesting a very rough “map” of the field and a few references to get started.

      +

      Keep in mind that although I studied it during my graduate studies, this is not my primary area of expertise (I’m a data scientist by trade), and I definitely don’t pretend to know everything in OR. This is a field too vast for any single person to understand in its entirety, and I talk mostly from a “amateur mathematician and computer scientist” standpoint.

      +

      Why is it hard to approach?

      +

      Operations research can be difficult to approach, since there are many references and subfields. Compared to machine learning for instance, OR has a slightly longer history (going back to the 17th century, for example with Monge and the optimal transport problem) For a very nice introduction (in French) to optimal transport, see these blog posts by Gabriel Peyré, on the CNRS maths blog: Part 1 and Part 2. See also the resources on optimaltransport.github.io (in English).
      +
      +      . This means that good textbooks and such have existed for a long time, but also that there will be plenty of material to choose from.

      +

      Moreover, OR is very close to applications. Sometimes methods may vary a lot in their presentation depending on whether they’re applied to train tracks, sudoku, or travelling salesmen. In practice, the terminology and notations are not the same everywhere. This is disconcerting if you are used to “pure” mathematics, where notations evolved over a long time and is pretty much standardised for many areas. In contrast, if you’re used to the statistics literature with its strange notations, you will find that OR is actually very well formalized.

      +

      There are many subfields of operations research, including all kinds of optimization (constrained and unconstrained), game theory, dynamic programming, stochastic processes, etc.

      +

      Where to start

      +

      For an overall introduction, I recommend Wentzel (1988). It is an old book, published by Mir Publications, a Soviet publisher which published many excellent scientific textbooks Mir also published Physics for Everyone by Lev Landau and Alexander Kitaigorodsky, a three-volume introduction to physics that is really accessible. Together with Feynman’s famous lectures, I read them (in French) when I was a kid, and it was the best introduction I could possibly have to the subject.
      +
      +      . It is out of print, but it is available on Archive.org. The book is quite old, but everything presented is still extremely relevant today. It requires absolutely no background, and covers everything: a general introduction to the field, linear programming, dynamic programming, Markov processes and queues, Monte Carlo methods, and game theory. Even if you already know some of these topics, the presentations is so clear that it is a pleasure to read! (In particular, it is one of the best presentations of dynamic programming that I have ever read. The explanation of the simplex algorithm is also excellent.)

      +
        +
      • why it may be more difficult to approach than other, more recent areas like ML and DL +
          +
        • slightly longer history
          • +
        • always very close to applications: somehow more “messy” in its notations, vocabulary, standard references, etc, as other “purer” fields of maths (similar to stats in this regard)
          • +
        • often approached from a applied point of view means that many very different concepts are often mixed together
          • +
        • +
      • why it is interesting and you should pursue it anyway +
          +
        • history of the field
          • +
        • examples of applications
          • +
        • theory perspective, rigorous field
          • +
        • +
      • different subfields +
          +
        • optimisation: constrained and unconstrained
          • +
        • game theory
          • +
        • dynamic programming
          • +
        • stochastic processes
          • +
        • simulation
          • +
        • +
      • how to learn and practice +
          +
        • references
          • +
        • courses
          • +
        • computational assets
          • +
        • +
      +

      References

      +
      +
      +

      Wentzel, Elena S. 1988. Operations Research: A Methodological Approach. Moscow: Mir publishers.

      +
      +
      +
      + +]]>       +       + ICLR 2020 Notes: Speakers and Workshops https://www.lozeve.com/posts/iclr-2020-notes.html @@ -65,52 +126,6 @@ ]]> - - Operations Research and Optimisation: where to start? - - https://www.lozeve.com/posts/operations-research-references.html - 2020-04-08T00:00:00Z - 2020-04-08T00:00:00Z - -
      - -
      -
      -

      Operations research (OR) is a vast area comprising a lot of theory, different branches of mathematics, and too many applications to count. In this post, I will try to explain why I find it so fascinating, but also why it can be a little disconcerting to explore at first. Then I will try to ease the newcomer’s path in this rich area, by suggesting a very rough “map” of the field and a few references to get started.

      -

      Keep in mind that although I studied it during my graduate studies, this is not my primary area of expertise (I’m a data scientist by trade), and I definitely don’t pretend to know everything in OR. This is a field too vast for any single person to understand in its entirety, and I talk mostly from a “amateur mathematician and computer scientist” standpoint.

      -

      Why is it hard to approach?

      -
        -
      • why it may be more difficult to approach than other, more recent areas like ML and DL -
          -
        • slightly longer history
          • -
        • always very close to applications: somehow more “messy” in its notations, vocabulary, standard references, etc, as other “purer” fields of maths (similar to stats in this regard)
          • -
        • often approached from a applied point of view means that many very different concepts are often mixed together
          • -
        • -
      • why it is interesting and you should pursue it anyway -
          -
        • history of the field
          • -
        • examples of applications
          • -
        • theory perspective, rigorous field
          • -
        • -
      • different subfields -
          -
        • optimisation: constrained and unconstrained
          • -
        • game theory
          • -
        • dynamic programming
          • -
        • stochastic processes
          • -
        • simulation
          • -
        • -
      • how to learn and practice -
          -
        • references
          • -
        • courses
          • -
        • computational assets
          • -
        • -
      -
      - -]]>       -       Reading notes: Hierarchical Optimal Transport for Document Representation diff --git a/_site/index.html b/_site/index.html index 2a7c926..6250f24 100644 --- a/_site/index.html +++ b/_site/index.html @@ -71,11 +71,11 @@ public key: RWQ6uexORp8f7USHA7nX9lFfltaCA9x6aBV06MvgiGjUt6BVf6McyD26
      • - ICLR 2020 Notes: Speakers and Workshops - May 5, 2020 + Operations Research and Optimisation: where to start? - May 26, 2020
      • - Operations Research and Optimisation: where to start? - April 8, 2020 + ICLR 2020 Notes: Speakers and Workshops - May 5, 2020
      • diff --git a/_site/posts/operations-research-references.html b/_site/posts/operations-research-references.html index c522320..3ed9b51 100644 --- a/_site/posts/operations-research-references.html +++ b/_site/posts/operations-research-references.html @@ -36,7 +36,7 @@

        Operations Research and Optimisation: where to start?

        -

        April 8, 2020

        +

        May 26, 2020

        @@ -52,6 +52,15 @@

        Operations research (OR) is a vast area comprising a lot of theory, different branches of mathematics, and too many applications to count. In this post, I will try to explain why I find it so fascinating, but also why it can be a little disconcerting to explore at first. Then I will try to ease the newcomer’s path in this rich area, by suggesting a very rough “map” of the field and a few references to get started.

        Keep in mind that although I studied it during my graduate studies, this is not my primary area of expertise (I’m a data scientist by trade), and I definitely don’t pretend to know everything in OR. This is a field too vast for any single person to understand in its entirety, and I talk mostly from a “amateur mathematician and computer scientist” standpoint.

        Why is it hard to approach?

        +

        Operations research can be difficult to approach, since there are many references and subfields. Compared to machine learning for instance, OR has a slightly longer history (going back to the 17th century, for example with Monge and the optimal transport problem) For a very nice introduction (in French) to optimal transport, see these blog posts by Gabriel Peyré, on the CNRS maths blog: Part 1 and Part 2. See also the resources on optimaltransport.github.io (in English).
        +
        +        . This means that good textbooks and such have existed for a long time, but also that there will be plenty of material to choose from.

        +

        Moreover, OR is very close to applications. Sometimes methods may vary a lot in their presentation depending on whether they’re applied to train tracks, sudoku, or travelling salesmen. In practice, the terminology and notations are not the same everywhere. This is disconcerting if you are used to “pure” mathematics, where notations evolved over a long time and is pretty much standardised for many areas. In contrast, if you’re used to the statistics literature with its strange notations, you will find that OR is actually very well formalized.

        +

        There are many subfields of operations research, including all kinds of optimization (constrained and unconstrained), game theory, dynamic programming, stochastic processes, etc.

        +

        Where to start

        +

        For an overall introduction, I recommend Wentzel (1988). It is an old book, published by Mir Publications, a Soviet publisher which published many excellent scientific textbooks Mir also published Physics for Everyone by Lev Landau and Alexander Kitaigorodsky, a three-volume introduction to physics that is really accessible. Together with Feynman’s famous lectures, I read them (in French) when I was a kid, and it was the best introduction I could possibly have to the subject.
        +
        +        . It is out of print, but it is available on Archive.org. The book is quite old, but everything presented is still extremely relevant today. It requires absolutely no background, and covers everything: a general introduction to the field, linear programming, dynamic programming, Markov processes and queues, Monte Carlo methods, and game theory. Even if you already know some of these topics, the presentations is so clear that it is a pleasure to read! (In particular, it is one of the best presentations of dynamic programming that I have ever read. The explanation of the simplex algorithm is also excellent.)

        • why it may be more difficult to approach than other, more recent areas like ML and DL
            @@ -80,6 +89,12 @@
          • computational assets
        +

        References

        +
        +
        +

        Wentzel, Elena S. 1988. Operations Research: A Methodological Approach. Moscow: Mir publishers.

        +
        +
        diff --git a/_site/rss.xml b/_site/rss.xml index 315b9c7..08a052f 100644 --- a/_site/rss.xml +++ b/_site/rss.xml @@ -7,8 +7,69 @@ - Tue, 05 May 2020 00:00:00 UT + Tue, 26 May 2020 00:00:00 UT + Operations Research and Optimisation: where to start? + https://www.lozeve.com/posts/operations-research-references.html + +
        + +
        +
        +

        Operations research (OR) is a vast area comprising a lot of theory, different branches of mathematics, and too many applications to count. In this post, I will try to explain why I find it so fascinating, but also why it can be a little disconcerting to explore at first. Then I will try to ease the newcomer’s path in this rich area, by suggesting a very rough “map” of the field and a few references to get started.

        +

        Keep in mind that although I studied it during my graduate studies, this is not my primary area of expertise (I’m a data scientist by trade), and I definitely don’t pretend to know everything in OR. This is a field too vast for any single person to understand in its entirety, and I talk mostly from a “amateur mathematician and computer scientist” standpoint.

        +

        Why is it hard to approach?

        +

        Operations research can be difficult to approach, since there are many references and subfields. Compared to machine learning for instance, OR has a slightly longer history (going back to the 17th century, for example with Monge and the optimal transport problem) For a very nice introduction (in French) to optimal transport, see these blog posts by Gabriel Peyré, on the CNRS maths blog: Part 1 and Part 2. See also the resources on optimaltransport.github.io (in English).
        +
        +        . This means that good textbooks and such have existed for a long time, but also that there will be plenty of material to choose from.

        +

        Moreover, OR is very close to applications. Sometimes methods may vary a lot in their presentation depending on whether they’re applied to train tracks, sudoku, or travelling salesmen. In practice, the terminology and notations are not the same everywhere. This is disconcerting if you are used to “pure” mathematics, where notations evolved over a long time and is pretty much standardised for many areas. In contrast, if you’re used to the statistics literature with its strange notations, you will find that OR is actually very well formalized.

        +

        There are many subfields of operations research, including all kinds of optimization (constrained and unconstrained), game theory, dynamic programming, stochastic processes, etc.

        +

        Where to start

        +

        For an overall introduction, I recommend Wentzel (1988). It is an old book, published by Mir Publications, a Soviet publisher which published many excellent scientific textbooks Mir also published Physics for Everyone by Lev Landau and Alexander Kitaigorodsky, a three-volume introduction to physics that is really accessible. Together with Feynman’s famous lectures, I read them (in French) when I was a kid, and it was the best introduction I could possibly have to the subject.
        +
        +        . It is out of print, but it is available on Archive.org. The book is quite old, but everything presented is still extremely relevant today. It requires absolutely no background, and covers everything: a general introduction to the field, linear programming, dynamic programming, Markov processes and queues, Monte Carlo methods, and game theory. Even if you already know some of these topics, the presentations is so clear that it is a pleasure to read! (In particular, it is one of the best presentations of dynamic programming that I have ever read. The explanation of the simplex algorithm is also excellent.)

        +
          +
        • why it may be more difficult to approach than other, more recent areas like ML and DL +
            +
          • slightly longer history
            • +
          • always very close to applications: somehow more “messy” in its notations, vocabulary, standard references, etc, as other “purer” fields of maths (similar to stats in this regard)
            • +
          • often approached from a applied point of view means that many very different concepts are often mixed together
            • +
          • +
        • why it is interesting and you should pursue it anyway +
            +
          • history of the field
            • +
          • examples of applications
            • +
          • theory perspective, rigorous field
            • +
          • +
        • different subfields +
            +
          • optimisation: constrained and unconstrained
            • +
          • game theory
            • +
          • dynamic programming
            • +
          • stochastic processes
            • +
          • simulation
            • +
          • +
        • how to learn and practice +
            +
          • references
            • +
          • courses
            • +
          • computational assets
            • +
          • +
        +

        References

        +
        +
        +

        Wentzel, Elena S. 1988. Operations Research: A Methodological Approach. Moscow: Mir publishers.

        +
        +
        +
        + +]]>         + Tue, 26 May 2020 00:00:00 UT + https://www.lozeve.com/posts/operations-research-references.html + Dimitri Lozeve +         + ICLR 2020 Notes: Speakers and Workshops https://www.lozeve.com/posts/iclr-2020-notes.html @@ -64,52 +125,6 @@ https://www.lozeve.com/posts/iclr-2020-notes.html Dimitri Lozeve - - Operations Research and Optimisation: where to start? - https://www.lozeve.com/posts/operations-research-references.html - -
        - -
        -
        -

        Operations research (OR) is a vast area comprising a lot of theory, different branches of mathematics, and too many applications to count. In this post, I will try to explain why I find it so fascinating, but also why it can be a little disconcerting to explore at first. Then I will try to ease the newcomer’s path in this rich area, by suggesting a very rough “map” of the field and a few references to get started.

        -

        Keep in mind that although I studied it during my graduate studies, this is not my primary area of expertise (I’m a data scientist by trade), and I definitely don’t pretend to know everything in OR. This is a field too vast for any single person to understand in its entirety, and I talk mostly from a “amateur mathematician and computer scientist” standpoint.

        -

        Why is it hard to approach?

        -
          -
        • why it may be more difficult to approach than other, more recent areas like ML and DL -
            -
          • slightly longer history
            • -
          • always very close to applications: somehow more “messy” in its notations, vocabulary, standard references, etc, as other “purer” fields of maths (similar to stats in this regard)
            • -
          • often approached from a applied point of view means that many very different concepts are often mixed together
            • -
          • -
        • why it is interesting and you should pursue it anyway -
            -
          • history of the field
            • -
          • examples of applications
            • -
          • theory perspective, rigorous field
            • -
          • -
        • different subfields -
            -
          • optimisation: constrained and unconstrained
            • -
          • game theory
            • -
          • dynamic programming
            • -
          • stochastic processes
            • -
          • simulation
            • -
          • -
        • how to learn and practice -
            -
          • references
            • -
          • courses
            • -
          • computational assets
            • -
          • -
        -
        - -]]>         - Wed, 08 Apr 2020 00:00:00 UT - https://www.lozeve.com/posts/operations-research-references.html - Dimitri Lozeve -         Reading notes: Hierarchical Optimal Transport for Document Representation https://www.lozeve.com/posts/hierarchical-optimal-transport-for-document-classification.html diff --git a/bib/bibliography.bib b/bib/bibliography.bib index 68fa7e2..7b7157c 100644 --- a/bib/bibliography.bib +++ b/bib/bibliography.bib @@ -185,3 +185,11 @@ author = {Mikolov, Tomas and Sutskever, Ilya and Chen, Kai and Corrado, Greg S and Dean, Jeff}, } +@book{wentzel1988_operat, + author = {Wentzel, Elena S.}, + title = {Operations research: a methodological approach}, + year = {1988}, + publisher = {Mir publishers}, + address = {Moscow}, + isbn = {9785030002279}, +} diff --git a/posts/operations-research-references.org b/posts/operations-research-references.org index 96cb972..7746ee5 100644 --- a/posts/operations-research-references.org +++ b/posts/operations-research-references.org @@ -1,6 +1,6 @@ --- title: "Operations Research and Optimisation: where to start?" -date: 2020-04-08 +date: 2020-05-26 --- [[https://en.wikipedia.org/wiki/Operations_research][Operations research]] (OR) is a vast area comprising a lot of theory, @@ -23,18 +23,53 @@ scientist" standpoint. Operations research can be difficult to approach, since there are many references and subfields. Compared to machine learning for instance, OR has a slightly longer history (going back to the 17th century, for -example with Monge and the optimal transport problem). This means that -good textbooks and such have existed for a long time, but also that -there will be plenty of material to choose from. +example with [[https://en.wikipedia.org/wiki/Gaspard_Monge][Monge]] and the [[https://en.wikipedia.org/wiki/Transportation_theory_(mathematics)][optimal transport +problem]])[fn:optimaltransport]. This means that good textbooks and such +have existed for a long time, but also that there will be plenty of +material to choose from. + +[fn:optimaltransport] {-} For a very nice introduction (in French) to +optimal transport, see these blog posts by [[https://twitter.com/gabrielpeyre][Gabriel Peyré]], on the CNRS +maths blog: [[https://images.math.cnrs.fr/Le-transport-optimal-numerique-et-ses-applications-Partie-1.html][Part 1]] and [[https://images.math.cnrs.fr/Le-transport-optimal-numerique-et-ses-applications-Partie-2.html][Part 2]]. See also the resources on +[[https://optimaltransport.github.io/][optimaltransport.github.io]] (in English). + Moreover, OR is very close to applications. Sometimes methods may vary a lot in their presentation depending on whether they're applied to train tracks, sudoku, or travelling salesmen. In practice, the terminology and notations are not the same everywhere. This is -disconcerting if you are used to mathematics, where notations evolved -over a long time and is pretty much standardised for many areas. In -contrast, if you're used to the statistics literature with its [[https://lingpipe-blog.com/2009/10/13/whats-wrong-with-probability-notation/][strange -notations]], you will find that OR is actually very well formalised. +disconcerting if you are used to "pure" mathematics, where notations +evolved over a long time and is pretty much standardised for many +areas. In contrast, if you're used to the statistics literature with +its [[https://lingpipe-blog.com/2009/10/13/whats-wrong-with-probability-notation/][strange notations]], you will find that OR is actually very well +formalized. + +There are many subfields of operations research, including all kinds +of optimization (constrained and unconstrained), game theory, dynamic +programming, stochastic processes, etc. + +* Where to start + +For an overall introduction, I recommend cite:wentzel1988_operat. It +is an old book, published by Mir Publications, a Soviet publisher +which published many excellent scientific textbooks[fn:mir]. It is out +of print, but it is available [[https://archive.org/details/WentzelOperationsResearchMir1983][on Archive.org]]. The book is quite old, +but everything presented is still extremely relevant today. It +requires absolutely no background, and covers everything: a general +introduction to the field, linear programming, dynamic programming, +Markov processes and queues, Monte Carlo methods, and game +theory. Even if you already know some of these topics, the +presentations is so clear that it is a pleasure to read! (In +particular, it is one of the best presentations of dynamic programming +that I have ever read. The explanation of the simplex algorithm is +also excellent.) + +[fn:mir] {-} Mir also published [[https://mirtitles.org/2011/06/03/physics-for-everyone/][/Physics for Everyone/]] by Lev Landau +and Alexander Kitaigorodsky, a three-volume introduction to physics +that is really accessible. Together with Feynman's famous [[https://www.feynmanlectures.caltech.edu/][lectures]], I +read them (in French) when I was a kid, and it was the best +introduction I could possibly have to the subject. + - why it may be more difficult to approach than other, more recent areas like ML and DL @@ -58,3 +93,5 @@ notations]], you will find that OR is actually very well formalised. - references - courses - computational assets + +* References From 72225bcbce07d8e28fcd6e4c2f8643e56cc4eee4 Mon Sep 17 00:00:00 2001 From: Dimitri Lozeve Date: Tue, 26 May 2020 16:52:01 +0200 Subject: [PATCH 4/9] Add modelling references --- _site/atom.xml | 38 ++++-------- .../posts/operations-research-references.html | 38 ++++-------- _site/rss.xml | 38 ++++-------- bib/bibliography.bib | 10 ++++ posts/operations-research-references.org | 59 ++++++++++++------- 5 files changed, 77 insertions(+), 106 deletions(-) diff --git a/_site/atom.xml b/_site/atom.xml index 9d2970c..b9058bc 100644 --- a/_site/atom.xml +++ b/_site/atom.xml @@ -29,42 +29,24 @@

        Moreover, OR is very close to applications. Sometimes methods may vary a lot in their presentation depending on whether they’re applied to train tracks, sudoku, or travelling salesmen. In practice, the terminology and notations are not the same everywhere. This is disconcerting if you are used to “pure” mathematics, where notations evolved over a long time and is pretty much standardised for many areas. In contrast, if you’re used to the statistics literature with its strange notations, you will find that OR is actually very well formalized.

        There are many subfields of operations research, including all kinds of optimization (constrained and unconstrained), game theory, dynamic programming, stochastic processes, etc.

        Where to start

        +

        Introduction and modelling

        For an overall introduction, I recommend Wentzel (1988). It is an old book, published by Mir Publications, a Soviet publisher which published many excellent scientific textbooks Mir also published Physics for Everyone by Lev Landau and Alexander Kitaigorodsky, a three-volume introduction to physics that is really accessible. Together with Feynman’s famous lectures, I read them (in French) when I was a kid, and it was the best introduction I could possibly have to the subject.

        . It is out of print, but it is available on Archive.org. The book is quite old, but everything presented is still extremely relevant today. It requires absolutely no background, and covers everything: a general introduction to the field, linear programming, dynamic programming, Markov processes and queues, Monte Carlo methods, and game theory. Even if you already know some of these topics, the presentations is so clear that it is a pleasure to read! (In particular, it is one of the best presentations of dynamic programming that I have ever read. The explanation of the simplex algorithm is also excellent.)

        -
          -
        • why it may be more difficult to approach than other, more recent areas like ML and DL -
            -
          • slightly longer history
            • -
          • always very close to applications: somehow more “messy” in its notations, vocabulary, standard references, etc, as other “purer” fields of maths (similar to stats in this regard)
            • -
          • often approached from a applied point of view means that many very different concepts are often mixed together
            • -
          • -
        • why it is interesting and you should pursue it anyway -
            -
          • history of the field
            • -
          • examples of applications
            • -
          • theory perspective, rigorous field
            • -
          • -
        • different subfields -
            -
          • optimisation: constrained and unconstrained
            • -
          • game theory
            • -
          • dynamic programming
            • -
          • stochastic processes
            • -
          • simulation
            • -
          • -
        • how to learn and practice -
            -
          • references
            • -
          • courses
            • -
          • computational assets
            • -
          • -
        +

        If you are interested in optimization, the first thing you have to learn is modelling, i.e. transforming your problem (described in natural language, often from a particular industrial application) into a mathematical programme. The mathematical programme is the structure on which you will be able to apply an algorithm to find an optimal solution. Even if (like me) you are initially more interested by the algorithmic side of things, learning to create models will shed a lot of light on the overall process, and will give you more insight in general on the reasoning behind algorithms.

        +

        The best book I have read on the subject is Williams (2013). It contains a lot of concrete, step-by-step examples on concrete applications, in a multitude of domains, and remains very easy to read and to follow. It covers nearly every type of problem, so it is very useful as a reference. When you encounter a concrete problem in real life afterwards, you will know how to construct an appropriate model, and in the process you will often identify a common type of problem. The book then gives plenty of advice on how to best approach each type of problem. Finally, it is also a great resource to build a “mental map” of the field, avoiding to get lost in the jungle of linear, stochastic, mixed integer, quadratic, and other network problems.

        +

        Another interesting resource is the freely available MOSEK Modeling Cookbook, covering many types of problems, with more mathematical details than in Williams (2013). It is built for people wanting to use the commercial MOSEK solver, so it could be useful if you plan to use a solver package like this one (more details on solvers below).

        +

        Theory and algorithms

        +

        Online courses

        +

        Solvers and computational resources

        References

        Wentzel, Elena S. 1988. Operations Research: A Methodological Approach. Moscow: Mir publishers.

        +
        +

        Williams, H. Paul. 2013. Model Building in Mathematical Programming. Chichester, West Sussex: Wiley. https://www.wiley.com/en-fr/Model+Building+in+Mathematical+Programming,+5th+Edition-p-9781118443330.

        +
        diff --git a/_site/posts/operations-research-references.html b/_site/posts/operations-research-references.html index 3ed9b51..347a5c1 100644 --- a/_site/posts/operations-research-references.html +++ b/_site/posts/operations-research-references.html @@ -58,42 +58,24 @@

        Moreover, OR is very close to applications. Sometimes methods may vary a lot in their presentation depending on whether they’re applied to train tracks, sudoku, or travelling salesmen. In practice, the terminology and notations are not the same everywhere. This is disconcerting if you are used to “pure” mathematics, where notations evolved over a long time and is pretty much standardised for many areas. In contrast, if you’re used to the statistics literature with its strange notations, you will find that OR is actually very well formalized.

        There are many subfields of operations research, including all kinds of optimization (constrained and unconstrained), game theory, dynamic programming, stochastic processes, etc.

        Where to start

        +

        Introduction and modelling

        For an overall introduction, I recommend Wentzel (1988). It is an old book, published by Mir Publications, a Soviet publisher which published many excellent scientific textbooks Mir also published Physics for Everyone by Lev Landau and Alexander Kitaigorodsky, a three-volume introduction to physics that is really accessible. Together with Feynman’s famous lectures, I read them (in French) when I was a kid, and it was the best introduction I could possibly have to the subject.

        . It is out of print, but it is available on Archive.org. The book is quite old, but everything presented is still extremely relevant today. It requires absolutely no background, and covers everything: a general introduction to the field, linear programming, dynamic programming, Markov processes and queues, Monte Carlo methods, and game theory. Even if you already know some of these topics, the presentations is so clear that it is a pleasure to read! (In particular, it is one of the best presentations of dynamic programming that I have ever read. The explanation of the simplex algorithm is also excellent.)

        -
          -
        • why it may be more difficult to approach than other, more recent areas like ML and DL -
            -
          • slightly longer history
            • -
          • always very close to applications: somehow more “messy” in its notations, vocabulary, standard references, etc, as other “purer” fields of maths (similar to stats in this regard)
            • -
          • often approached from a applied point of view means that many very different concepts are often mixed together
            • -
          • -
        • why it is interesting and you should pursue it anyway -
            -
          • history of the field
            • -
          • examples of applications
            • -
          • theory perspective, rigorous field
            • -
          • -
        • different subfields -
            -
          • optimisation: constrained and unconstrained
            • -
          • game theory
            • -
          • dynamic programming
            • -
          • stochastic processes
            • -
          • simulation
            • -
          • -
        • how to learn and practice -
            -
          • references
            • -
          • courses
            • -
          • computational assets
            • -
          • -
        +

        If you are interested in optimization, the first thing you have to learn is modelling, i.e. transforming your problem (described in natural language, often from a particular industrial application) into a mathematical programme. The mathematical programme is the structure on which you will be able to apply an algorithm to find an optimal solution. Even if (like me) you are initially more interested by the algorithmic side of things, learning to create models will shed a lot of light on the overall process, and will give you more insight in general on the reasoning behind algorithms.

        +

        The best book I have read on the subject is Williams (2013). It contains a lot of concrete, step-by-step examples on concrete applications, in a multitude of domains, and remains very easy to read and to follow. It covers nearly every type of problem, so it is very useful as a reference. When you encounter a concrete problem in real life afterwards, you will know how to construct an appropriate model, and in the process you will often identify a common type of problem. The book then gives plenty of advice on how to best approach each type of problem. Finally, it is also a great resource to build a “mental map” of the field, avoiding to get lost in the jungle of linear, stochastic, mixed integer, quadratic, and other network problems.

        +

        Another interesting resource is the freely available MOSEK Modeling Cookbook, covering many types of problems, with more mathematical details than in Williams (2013). It is built for people wanting to use the commercial MOSEK solver, so it could be useful if you plan to use a solver package like this one (more details on solvers below).

        +

        Theory and algorithms

        +

        Online courses

        +

        Solvers and computational resources

        References

        Wentzel, Elena S. 1988. Operations Research: A Methodological Approach. Moscow: Mir publishers.

        +
        +

        Williams, H. Paul. 2013. Model Building in Mathematical Programming. Chichester, West Sussex: Wiley. https://www.wiley.com/en-fr/Model+Building+in+Mathematical+Programming,+5th+Edition-p-9781118443330.

        +
        diff --git a/_site/rss.xml b/_site/rss.xml index 08a052f..d28c92a 100644 --- a/_site/rss.xml +++ b/_site/rss.xml @@ -25,42 +25,24 @@

        Moreover, OR is very close to applications. Sometimes methods may vary a lot in their presentation depending on whether they’re applied to train tracks, sudoku, or travelling salesmen. In practice, the terminology and notations are not the same everywhere. This is disconcerting if you are used to “pure” mathematics, where notations evolved over a long time and is pretty much standardised for many areas. In contrast, if you’re used to the statistics literature with its strange notations, you will find that OR is actually very well formalized.

        There are many subfields of operations research, including all kinds of optimization (constrained and unconstrained), game theory, dynamic programming, stochastic processes, etc.

        Where to start

        +

        Introduction and modelling

        For an overall introduction, I recommend Wentzel (1988). It is an old book, published by Mir Publications, a Soviet publisher which published many excellent scientific textbooks Mir also published Physics for Everyone by Lev Landau and Alexander Kitaigorodsky, a three-volume introduction to physics that is really accessible. Together with Feynman’s famous lectures, I read them (in French) when I was a kid, and it was the best introduction I could possibly have to the subject.

        . It is out of print, but it is available on Archive.org. The book is quite old, but everything presented is still extremely relevant today. It requires absolutely no background, and covers everything: a general introduction to the field, linear programming, dynamic programming, Markov processes and queues, Monte Carlo methods, and game theory. Even if you already know some of these topics, the presentations is so clear that it is a pleasure to read! (In particular, it is one of the best presentations of dynamic programming that I have ever read. The explanation of the simplex algorithm is also excellent.)

        -
          -
        • why it may be more difficult to approach than other, more recent areas like ML and DL -
            -
          • slightly longer history
            • -
          • always very close to applications: somehow more “messy” in its notations, vocabulary, standard references, etc, as other “purer” fields of maths (similar to stats in this regard)
            • -
          • often approached from a applied point of view means that many very different concepts are often mixed together
            • -
          • -
        • why it is interesting and you should pursue it anyway -
            -
          • history of the field
            • -
          • examples of applications
            • -
          • theory perspective, rigorous field
            • -
          • -
        • different subfields -
            -
          • optimisation: constrained and unconstrained
            • -
          • game theory
            • -
          • dynamic programming
            • -
          • stochastic processes
            • -
          • simulation
            • -
          • -
        • how to learn and practice -
            -
          • references
            • -
          • courses
            • -
          • computational assets
            • -
          • -
        +

        If you are interested in optimization, the first thing you have to learn is modelling, i.e. transforming your problem (described in natural language, often from a particular industrial application) into a mathematical programme. The mathematical programme is the structure on which you will be able to apply an algorithm to find an optimal solution. Even if (like me) you are initially more interested by the algorithmic side of things, learning to create models will shed a lot of light on the overall process, and will give you more insight in general on the reasoning behind algorithms.

        +

        The best book I have read on the subject is Williams (2013). It contains a lot of concrete, step-by-step examples on concrete applications, in a multitude of domains, and remains very easy to read and to follow. It covers nearly every type of problem, so it is very useful as a reference. When you encounter a concrete problem in real life afterwards, you will know how to construct an appropriate model, and in the process you will often identify a common type of problem. The book then gives plenty of advice on how to best approach each type of problem. Finally, it is also a great resource to build a “mental map” of the field, avoiding to get lost in the jungle of linear, stochastic, mixed integer, quadratic, and other network problems.

        +

        Another interesting resource is the freely available MOSEK Modeling Cookbook, covering many types of problems, with more mathematical details than in Williams (2013). It is built for people wanting to use the commercial MOSEK solver, so it could be useful if you plan to use a solver package like this one (more details on solvers below).

        +

        Theory and algorithms

        +

        Online courses

        +

        Solvers and computational resources

        References

        Wentzel, Elena S. 1988. Operations Research: A Methodological Approach. Moscow: Mir publishers.

        +
        +

        Williams, H. Paul. 2013. Model Building in Mathematical Programming. Chichester, West Sussex: Wiley. https://www.wiley.com/en-fr/Model+Building+in+Mathematical+Programming,+5th+Edition-p-9781118443330.

        +
        diff --git a/bib/bibliography.bib b/bib/bibliography.bib index 7b7157c..8bac017 100644 --- a/bib/bibliography.bib +++ b/bib/bibliography.bib @@ -193,3 +193,13 @@ address = {Moscow}, isbn = {9785030002279}, } + +@book{williams2013_model, + author = {Williams, H. Paul}, + title = {Model building in mathematical programming}, + year = {2013}, + publisher = {Wiley}, + url = {https://www.wiley.com/en-fr/Model+Building+in+Mathematical+Programming,+5th+Edition-p-9781118443330}, + address = {Chichester, West Sussex}, + isbn = {9781118443330}, +} diff --git a/posts/operations-research-references.org b/posts/operations-research-references.org index 7746ee5..b8b376b 100644 --- a/posts/operations-research-references.org +++ b/posts/operations-research-references.org @@ -50,6 +50,8 @@ programming, stochastic processes, etc. * Where to start +** Introduction and modelling + For an overall introduction, I recommend cite:wentzel1988_operat. It is an old book, published by Mir Publications, a Soviet publisher which published many excellent scientific textbooks[fn:mir]. It is out @@ -71,27 +73,40 @@ read them (in French) when I was a kid, and it was the best introduction I could possibly have to the subject. -- why it may be more difficult to approach than other, more recent - areas like ML and DL - - slightly longer history - - always very close to applications: somehow more "messy" in its - notations, vocabulary, standard references, etc, as other "purer" - fields of maths (similar to stats in this regard) - - often approached from a applied point of view means that many very - different concepts are often mixed together -- why it is interesting and you should pursue it anyway - - history of the field - - examples of applications - - theory perspective, rigorous field -- different subfields - - optimisation: constrained and unconstrained - - game theory - - dynamic programming - - stochastic processes - - simulation -- how to learn and practice - - references - - courses - - computational assets +If you are interested in optimization, the first thing you have to +learn is modelling, i.e. transforming your problem (described in +natural language, often from a particular industrial application) into +a mathematical programme. The mathematical programme is the structure +on which you will be able to apply an algorithm to find an optimal +solution. Even if (like me) you are initially more interested by the +algorithmic side of things, learning to create models will shed a lot +of light on the overall process, and will give you more insight in +general on the reasoning behind algorithms. + +The best book I have read on the subject is +cite:williams2013_model. It contains a lot of concrete, step-by-step +examples on concrete applications, in a multitude of domains, and +remains very easy to read and to follow. It covers nearly every type +of problem, so it is very useful as a reference. When you encounter a +concrete problem in real life afterwards, you will know how to +construct an appropriate model, and in the process you will often +identify a common type of problem. The book then gives plenty of +advice on how to best approach each type of problem. Finally, it is +also a great resource to build a "mental map" of the field, avoiding +to get lost in the jungle of linear, stochastic, mixed integer, +quadratic, and other network problems. + +Another interesting resource is the freely available [[https://docs.mosek.com/modeling-cookbook/index.html][MOSEK Modeling +Cookbook]], covering many types of problems, with more mathematical +details than in cite:williams2013_model. It is built for people +wanting to use the commercial [[https://www.mosek.com/][MOSEK]] solver, so it could be useful if +you plan to use a solver package like this one (more details on +solvers [[solvers][below]]). + +** Theory and algorithms + +** Online courses + +* Solvers and computational resources <> * References From dd63a5ec2a623ca8f2947a3a121315b0003fa5c1 Mon Sep 17 00:00:00 2001 From: Dimitri Lozeve Date: Tue, 26 May 2020 18:06:23 +0200 Subject: [PATCH 5/9] Add references for other optimization problems --- _site/atom.xml | 53 ++++++++++-- .../posts/operations-research-references.html | 49 +++++++++-- _site/rss.xml | 53 ++++++++++-- bib/bibliography.bib | 85 +++++++++++++++++++ posts/operations-research-references.org | 36 ++++++++ 5 files changed, 251 insertions(+), 25 deletions(-) diff --git a/_site/atom.xml b/_site/atom.xml index b9058bc..49b53cd 100644 --- a/_site/atom.xml +++ b/_site/atom.xml @@ -22,25 +22,60 @@

        Operations research (OR) is a vast area comprising a lot of theory, different branches of mathematics, and too many applications to count. In this post, I will try to explain why I find it so fascinating, but also why it can be a little disconcerting to explore at first. Then I will try to ease the newcomer’s path in this rich area, by suggesting a very rough “map” of the field and a few references to get started.

        Keep in mind that although I studied it during my graduate studies, this is not my primary area of expertise (I’m a data scientist by trade), and I definitely don’t pretend to know everything in OR. This is a field too vast for any single person to understand in its entirety, and I talk mostly from a “amateur mathematician and computer scientist” standpoint.

        -

        Why is it hard to approach?

        -

        Operations research can be difficult to approach, since there are many references and subfields. Compared to machine learning for instance, OR has a slightly longer history (going back to the 17th century, for example with Monge and the optimal transport problem) For a very nice introduction (in French) to optimal transport, see these blog posts by Gabriel Peyré, on the CNRS maths blog: Part 1 and Part 2. See also the resources on optimaltransport.github.io (in English).
        +

        Why is it hard to approach?

        +

        Operations research can be difficult to approach, since there are many references and subfields. Compared to machine learning for instance, OR has a slightly longer history (going back to the 17th century, for example with Monge and the optimal transport problem) For a very nice introduction (in French) to optimal transport, see these blog posts by Gabriel Peyré, on the CNRS maths blog: Part 1 and Part 2. See also the resources on optimaltransport.github.io (in English).

        . This means that good textbooks and such have existed for a long time, but also that there will be plenty of material to choose from.

        Moreover, OR is very close to applications. Sometimes methods may vary a lot in their presentation depending on whether they’re applied to train tracks, sudoku, or travelling salesmen. In practice, the terminology and notations are not the same everywhere. This is disconcerting if you are used to “pure” mathematics, where notations evolved over a long time and is pretty much standardised for many areas. In contrast, if you’re used to the statistics literature with its strange notations, you will find that OR is actually very well formalized.

        There are many subfields of operations research, including all kinds of optimization (constrained and unconstrained), game theory, dynamic programming, stochastic processes, etc.

        -

        Where to start

        -

        Introduction and modelling

        -

        For an overall introduction, I recommend Wentzel (1988). It is an old book, published by Mir Publications, a Soviet publisher which published many excellent scientific textbooks Mir also published Physics for Everyone by Lev Landau and Alexander Kitaigorodsky, a three-volume introduction to physics that is really accessible. Together with Feynman’s famous lectures, I read them (in French) when I was a kid, and it was the best introduction I could possibly have to the subject.
        +

        Where to start

        +

        Introduction and modelling

        +

        For an overall introduction, I recommend Wentzel (1988). It is an old book, published by Mir Publications, a Soviet publisher which published many excellent scientific textbooks Mir also published Physics for Everyone by Lev Landau and Alexander Kitaigorodsky, a three-volume introduction to physics that is really accessible. Together with Feynman’s famous lectures, I read them (in French) when I was a kid, and it was the best introduction I could possibly have to the subject.

        . It is out of print, but it is available on Archive.org. The book is quite old, but everything presented is still extremely relevant today. It requires absolutely no background, and covers everything: a general introduction to the field, linear programming, dynamic programming, Markov processes and queues, Monte Carlo methods, and game theory. Even if you already know some of these topics, the presentations is so clear that it is a pleasure to read! (In particular, it is one of the best presentations of dynamic programming that I have ever read. The explanation of the simplex algorithm is also excellent.)

        If you are interested in optimization, the first thing you have to learn is modelling, i.e. transforming your problem (described in natural language, often from a particular industrial application) into a mathematical programme. The mathematical programme is the structure on which you will be able to apply an algorithm to find an optimal solution. Even if (like me) you are initially more interested by the algorithmic side of things, learning to create models will shed a lot of light on the overall process, and will give you more insight in general on the reasoning behind algorithms.

        The best book I have read on the subject is Williams (2013). It contains a lot of concrete, step-by-step examples on concrete applications, in a multitude of domains, and remains very easy to read and to follow. It covers nearly every type of problem, so it is very useful as a reference. When you encounter a concrete problem in real life afterwards, you will know how to construct an appropriate model, and in the process you will often identify a common type of problem. The book then gives plenty of advice on how to best approach each type of problem. Finally, it is also a great resource to build a “mental map” of the field, avoiding to get lost in the jungle of linear, stochastic, mixed integer, quadratic, and other network problems.

        Another interesting resource is the freely available MOSEK Modeling Cookbook, covering many types of problems, with more mathematical details than in Williams (2013). It is built for people wanting to use the commercial MOSEK solver, so it could be useful if you plan to use a solver package like this one (more details on solvers below).

        -

        Theory and algorithms

        -

        Online courses

        -

        Solvers and computational resources

        -

        References

        +

        Theory and algorithms

        +

        The basic algorithm for optimization is the simplex algorithm, developed by Dantzig in the 1940s to solve linear programming problems. It is the one of the main building blocks for mathematical optimization, and is used and referenced extensively in all kinds of approaches. As such, it is really important to understand it in detail. There are many books on the subject, but I especially liked Chvátal (1983) (out of print, but you can find cheap used versions on Amazon). It covers everything there is to know on the simplex algorithms (step-by-step explanations with simple examples, correctness and complexity analysis, computational and implementation considerations) and to many applications. I think it is overall the best introduction. Vanderbei (2014) follows a very similar outline, but contains more recent computational considerationsFor all the details about practical implementations of the simplex algorithm, Maros (2003) is dedicated to the computational aspects and contains everything you will need.
        +
        +        . (The author also has lecture slides.)

        +

        For more books on linear programming, the two books Dantzig (1997), Dantzig (2003) are very complete, if somewhat more mathematically advanced. Bertsimas and Tsitsiklis (1997) is also a great reference, if you can find it.

        +

        For all the other subfields, this great StackExchange answer contains a lot of useful references, including most of the above. Of particular note are Peyré and Cuturi (2019) for optimal transport, Boyd (2004) for convex optimization (freely available online), and Nocedal (2006) for numerical optimization. Kochenderfer (2019) is not in the list (because it is very recent) but is also excellent, with examples in Julia covering nearly every kind of optimization algorithms.

        +

        Online courses

        +

        Solvers and computational resources

        +

        References

        +
        +

        Bertsimas, Dimitris, and John N. Tsitsiklis. 1997. Introduction to Linear Optimization. Belmont, Massachusetts: Athena Scientific. http://www.athenasc.com/linoptbook.html.

        +
        +
        +

        Boyd, Stephen. 2004. Convex Optimization. Cambridge, UK New York: Cambridge University Press.

        +
        +
        +

        Chvátal, Vašek. 1983. Linear Programming. New York: W.H. Freeman.

        +
        +
        +

        Dantzig, George. 1997. Linear Programming 1: Introduction. New York: Springer. https://www.springer.com/gp/book/9780387948331.

        +
        +
        +

        ———. 2003. Linear Programming 2: Theory and Extensions. New York: Springer. https://www.springer.com/gp/book/9780387986135.

        +
        +
        +

        Kochenderfer, Mykel. 2019. Algorithms for Optimization. Cambridge, Massachusetts: The MIT Press.

        +
        +
        +

        Maros, István. 2003. Computational Techniques of the Simplex Method. Boston: Kluwer Academic Publishers.

        +
        +
        +

        Nocedal, Jorge. 2006. Numerical Optimization. New York: Springer. https://www.springer.com/gp/book/9780387303031.

        +
        +
        +

        Peyré, Gabriel, and Marco Cuturi. 2019. “Computational Optimal Transport.” Foundations and Trends in Machine Learning 11 (5-6): 355–206. https://doi.org/10.1561/2200000073.

        +
        +
        +

        Vanderbei, Robert. 2014. Linear Programming : Foundations and Extensions. New York: Springer.

        +

        Wentzel, Elena S. 1988. Operations Research: A Methodological Approach. Moscow: Mir publishers.

        diff --git a/_site/posts/operations-research-references.html b/_site/posts/operations-research-references.html index 347a5c1..4a2cb9f 100644 --- a/_site/posts/operations-research-references.html +++ b/_site/posts/operations-research-references.html @@ -51,25 +51,60 @@

        Operations research (OR) is a vast area comprising a lot of theory, different branches of mathematics, and too many applications to count. In this post, I will try to explain why I find it so fascinating, but also why it can be a little disconcerting to explore at first. Then I will try to ease the newcomer’s path in this rich area, by suggesting a very rough “map” of the field and a few references to get started.

        Keep in mind that although I studied it during my graduate studies, this is not my primary area of expertise (I’m a data scientist by trade), and I definitely don’t pretend to know everything in OR. This is a field too vast for any single person to understand in its entirety, and I talk mostly from a “amateur mathematician and computer scientist” standpoint.

        -

        Why is it hard to approach?

        +

        Why is it hard to approach?

        Operations research can be difficult to approach, since there are many references and subfields. Compared to machine learning for instance, OR has a slightly longer history (going back to the 17th century, for example with Monge and the optimal transport problem) For a very nice introduction (in French) to optimal transport, see these blog posts by Gabriel Peyré, on the CNRS maths blog: Part 1 and Part 2. See also the resources on optimaltransport.github.io (in English).

        . This means that good textbooks and such have existed for a long time, but also that there will be plenty of material to choose from.

        Moreover, OR is very close to applications. Sometimes methods may vary a lot in their presentation depending on whether they’re applied to train tracks, sudoku, or travelling salesmen. In practice, the terminology and notations are not the same everywhere. This is disconcerting if you are used to “pure” mathematics, where notations evolved over a long time and is pretty much standardised for many areas. In contrast, if you’re used to the statistics literature with its strange notations, you will find that OR is actually very well formalized.

        There are many subfields of operations research, including all kinds of optimization (constrained and unconstrained), game theory, dynamic programming, stochastic processes, etc.

        -

        Where to start

        -

        Introduction and modelling

        +

        Where to start

        +

        Introduction and modelling

        For an overall introduction, I recommend Wentzel (1988). It is an old book, published by Mir Publications, a Soviet publisher which published many excellent scientific textbooks Mir also published Physics for Everyone by Lev Landau and Alexander Kitaigorodsky, a three-volume introduction to physics that is really accessible. Together with Feynman’s famous lectures, I read them (in French) when I was a kid, and it was the best introduction I could possibly have to the subject.

        . It is out of print, but it is available on Archive.org. The book is quite old, but everything presented is still extremely relevant today. It requires absolutely no background, and covers everything: a general introduction to the field, linear programming, dynamic programming, Markov processes and queues, Monte Carlo methods, and game theory. Even if you already know some of these topics, the presentations is so clear that it is a pleasure to read! (In particular, it is one of the best presentations of dynamic programming that I have ever read. The explanation of the simplex algorithm is also excellent.)

        If you are interested in optimization, the first thing you have to learn is modelling, i.e. transforming your problem (described in natural language, often from a particular industrial application) into a mathematical programme. The mathematical programme is the structure on which you will be able to apply an algorithm to find an optimal solution. Even if (like me) you are initially more interested by the algorithmic side of things, learning to create models will shed a lot of light on the overall process, and will give you more insight in general on the reasoning behind algorithms.

        The best book I have read on the subject is Williams (2013). It contains a lot of concrete, step-by-step examples on concrete applications, in a multitude of domains, and remains very easy to read and to follow. It covers nearly every type of problem, so it is very useful as a reference. When you encounter a concrete problem in real life afterwards, you will know how to construct an appropriate model, and in the process you will often identify a common type of problem. The book then gives plenty of advice on how to best approach each type of problem. Finally, it is also a great resource to build a “mental map” of the field, avoiding to get lost in the jungle of linear, stochastic, mixed integer, quadratic, and other network problems.

        Another interesting resource is the freely available MOSEK Modeling Cookbook, covering many types of problems, with more mathematical details than in Williams (2013). It is built for people wanting to use the commercial MOSEK solver, so it could be useful if you plan to use a solver package like this one (more details on solvers below).

        -

        Theory and algorithms

        -

        Online courses

        -

        Solvers and computational resources

        -

        References

        +

        Theory and algorithms

        +

        The basic algorithm for optimization is the simplex algorithm, developed by Dantzig in the 1940s to solve linear programming problems. It is the one of the main building blocks for mathematical optimization, and is used and referenced extensively in all kinds of approaches. As such, it is really important to understand it in detail. There are many books on the subject, but I especially liked Chvátal (1983) (out of print, but you can find cheap used versions on Amazon). It covers everything there is to know on the simplex algorithms (step-by-step explanations with simple examples, correctness and complexity analysis, computational and implementation considerations) and to many applications. I think it is overall the best introduction. Vanderbei (2014) follows a very similar outline, but contains more recent computational considerationsFor all the details about practical implementations of the simplex algorithm, Maros (2003) is dedicated to the computational aspects and contains everything you will need.
        +
        +        . (The author also has lecture slides.)

        +

        For more books on linear programming, the two books Dantzig (1997), Dantzig (2003) are very complete, if somewhat more mathematically advanced. Bertsimas and Tsitsiklis (1997) is also a great reference, if you can find it.

        +

        For all the other subfields, this great StackExchange answer contains a lot of useful references, including most of the above. Of particular note are Peyré and Cuturi (2019) for optimal transport, Boyd (2004) for convex optimization (freely available online), and Nocedal (2006) for numerical optimization. Kochenderfer (2019) is not in the list (because it is very recent) but is also excellent, with examples in Julia covering nearly every kind of optimization algorithms.

        +

        Online courses

        +

        Solvers and computational resources

        +

        References

        +
        +

        Bertsimas, Dimitris, and John N. Tsitsiklis. 1997. Introduction to Linear Optimization. Belmont, Massachusetts: Athena Scientific. http://www.athenasc.com/linoptbook.html.

        +
        +
        +

        Boyd, Stephen. 2004. Convex Optimization. Cambridge, UK New York: Cambridge University Press.

        +
        +
        +

        Chvátal, Vašek. 1983. Linear Programming. New York: W.H. Freeman.

        +
        +
        +

        Dantzig, George. 1997. Linear Programming 1: Introduction. New York: Springer. https://www.springer.com/gp/book/9780387948331.

        +
        +
        +

        ———. 2003. Linear Programming 2: Theory and Extensions. New York: Springer. https://www.springer.com/gp/book/9780387986135.

        +
        +
        +

        Kochenderfer, Mykel. 2019. Algorithms for Optimization. Cambridge, Massachusetts: The MIT Press.

        +
        +
        +

        Maros, István. 2003. Computational Techniques of the Simplex Method. Boston: Kluwer Academic Publishers.

        +
        +
        +

        Nocedal, Jorge. 2006. Numerical Optimization. New York: Springer. https://www.springer.com/gp/book/9780387303031.

        +
        +
        +

        Peyré, Gabriel, and Marco Cuturi. 2019. “Computational Optimal Transport.” Foundations and Trends in Machine Learning 11 (5-6): 355–206. https://doi.org/10.1561/2200000073.

        +
        +
        +

        Vanderbei, Robert. 2014. Linear Programming : Foundations and Extensions. New York: Springer.

        +

        Wentzel, Elena S. 1988. Operations Research: A Methodological Approach. Moscow: Mir publishers.

        diff --git a/_site/rss.xml b/_site/rss.xml index d28c92a..c273d5d 100644 --- a/_site/rss.xml +++ b/_site/rss.xml @@ -18,25 +18,60 @@

        Operations research (OR) is a vast area comprising a lot of theory, different branches of mathematics, and too many applications to count. In this post, I will try to explain why I find it so fascinating, but also why it can be a little disconcerting to explore at first. Then I will try to ease the newcomer’s path in this rich area, by suggesting a very rough “map” of the field and a few references to get started.

        Keep in mind that although I studied it during my graduate studies, this is not my primary area of expertise (I’m a data scientist by trade), and I definitely don’t pretend to know everything in OR. This is a field too vast for any single person to understand in its entirety, and I talk mostly from a “amateur mathematician and computer scientist” standpoint.

        -

        Why is it hard to approach?

        -

        Operations research can be difficult to approach, since there are many references and subfields. Compared to machine learning for instance, OR has a slightly longer history (going back to the 17th century, for example with Monge and the optimal transport problem) For a very nice introduction (in French) to optimal transport, see these blog posts by Gabriel Peyré, on the CNRS maths blog: Part 1 and Part 2. See also the resources on optimaltransport.github.io (in English).
        +

        Why is it hard to approach?

        +

        Operations research can be difficult to approach, since there are many references and subfields. Compared to machine learning for instance, OR has a slightly longer history (going back to the 17th century, for example with Monge and the optimal transport problem) For a very nice introduction (in French) to optimal transport, see these blog posts by Gabriel Peyré, on the CNRS maths blog: Part 1 and Part 2. See also the resources on optimaltransport.github.io (in English).

        . This means that good textbooks and such have existed for a long time, but also that there will be plenty of material to choose from.

        Moreover, OR is very close to applications. Sometimes methods may vary a lot in their presentation depending on whether they’re applied to train tracks, sudoku, or travelling salesmen. In practice, the terminology and notations are not the same everywhere. This is disconcerting if you are used to “pure” mathematics, where notations evolved over a long time and is pretty much standardised for many areas. In contrast, if you’re used to the statistics literature with its strange notations, you will find that OR is actually very well formalized.

        There are many subfields of operations research, including all kinds of optimization (constrained and unconstrained), game theory, dynamic programming, stochastic processes, etc.

        -

        Where to start

        -

        Introduction and modelling

        -

        For an overall introduction, I recommend Wentzel (1988). It is an old book, published by Mir Publications, a Soviet publisher which published many excellent scientific textbooks Mir also published Physics for Everyone by Lev Landau and Alexander Kitaigorodsky, a three-volume introduction to physics that is really accessible. Together with Feynman’s famous lectures, I read them (in French) when I was a kid, and it was the best introduction I could possibly have to the subject.
        +

        Where to start

        +

        Introduction and modelling

        +

        For an overall introduction, I recommend Wentzel (1988). It is an old book, published by Mir Publications, a Soviet publisher which published many excellent scientific textbooks Mir also published Physics for Everyone by Lev Landau and Alexander Kitaigorodsky, a three-volume introduction to physics that is really accessible. Together with Feynman’s famous lectures, I read them (in French) when I was a kid, and it was the best introduction I could possibly have to the subject.

        . It is out of print, but it is available on Archive.org. The book is quite old, but everything presented is still extremely relevant today. It requires absolutely no background, and covers everything: a general introduction to the field, linear programming, dynamic programming, Markov processes and queues, Monte Carlo methods, and game theory. Even if you already know some of these topics, the presentations is so clear that it is a pleasure to read! (In particular, it is one of the best presentations of dynamic programming that I have ever read. The explanation of the simplex algorithm is also excellent.)

        If you are interested in optimization, the first thing you have to learn is modelling, i.e. transforming your problem (described in natural language, often from a particular industrial application) into a mathematical programme. The mathematical programme is the structure on which you will be able to apply an algorithm to find an optimal solution. Even if (like me) you are initially more interested by the algorithmic side of things, learning to create models will shed a lot of light on the overall process, and will give you more insight in general on the reasoning behind algorithms.

        The best book I have read on the subject is Williams (2013). It contains a lot of concrete, step-by-step examples on concrete applications, in a multitude of domains, and remains very easy to read and to follow. It covers nearly every type of problem, so it is very useful as a reference. When you encounter a concrete problem in real life afterwards, you will know how to construct an appropriate model, and in the process you will often identify a common type of problem. The book then gives plenty of advice on how to best approach each type of problem. Finally, it is also a great resource to build a “mental map” of the field, avoiding to get lost in the jungle of linear, stochastic, mixed integer, quadratic, and other network problems.

        Another interesting resource is the freely available MOSEK Modeling Cookbook, covering many types of problems, with more mathematical details than in Williams (2013). It is built for people wanting to use the commercial MOSEK solver, so it could be useful if you plan to use a solver package like this one (more details on solvers below).

        -

        Theory and algorithms

        -

        Online courses

        -

        Solvers and computational resources

        -

        References

        +

        Theory and algorithms

        +

        The basic algorithm for optimization is the simplex algorithm, developed by Dantzig in the 1940s to solve linear programming problems. It is the one of the main building blocks for mathematical optimization, and is used and referenced extensively in all kinds of approaches. As such, it is really important to understand it in detail. There are many books on the subject, but I especially liked Chvátal (1983) (out of print, but you can find cheap used versions on Amazon). It covers everything there is to know on the simplex algorithms (step-by-step explanations with simple examples, correctness and complexity analysis, computational and implementation considerations) and to many applications. I think it is overall the best introduction. Vanderbei (2014) follows a very similar outline, but contains more recent computational considerationsFor all the details about practical implementations of the simplex algorithm, Maros (2003) is dedicated to the computational aspects and contains everything you will need.
        +
        +        . (The author also has lecture slides.)

        +

        For more books on linear programming, the two books Dantzig (1997), Dantzig (2003) are very complete, if somewhat more mathematically advanced. Bertsimas and Tsitsiklis (1997) is also a great reference, if you can find it.

        +

        For all the other subfields, this great StackExchange answer contains a lot of useful references, including most of the above. Of particular note are Peyré and Cuturi (2019) for optimal transport, Boyd (2004) for convex optimization (freely available online), and Nocedal (2006) for numerical optimization. Kochenderfer (2019) is not in the list (because it is very recent) but is also excellent, with examples in Julia covering nearly every kind of optimization algorithms.

        +

        Online courses

        +

        Solvers and computational resources

        +

        References

        +
        +

        Bertsimas, Dimitris, and John N. Tsitsiklis. 1997. Introduction to Linear Optimization. Belmont, Massachusetts: Athena Scientific. http://www.athenasc.com/linoptbook.html.

        +
        +
        +

        Boyd, Stephen. 2004. Convex Optimization. Cambridge, UK New York: Cambridge University Press.

        +
        +
        +

        Chvátal, Vašek. 1983. Linear Programming. New York: W.H. Freeman.

        +
        +
        +

        Dantzig, George. 1997. Linear Programming 1: Introduction. New York: Springer. https://www.springer.com/gp/book/9780387948331.

        +
        +
        +

        ———. 2003. Linear Programming 2: Theory and Extensions. New York: Springer. https://www.springer.com/gp/book/9780387986135.

        +
        +
        +

        Kochenderfer, Mykel. 2019. Algorithms for Optimization. Cambridge, Massachusetts: The MIT Press.

        +
        +
        +

        Maros, István. 2003. Computational Techniques of the Simplex Method. Boston: Kluwer Academic Publishers.

        +
        +
        +

        Nocedal, Jorge. 2006. Numerical Optimization. New York: Springer. https://www.springer.com/gp/book/9780387303031.

        +
        +
        +

        Peyré, Gabriel, and Marco Cuturi. 2019. “Computational Optimal Transport.” Foundations and Trends in Machine Learning 11 (5-6): 355–206. https://doi.org/10.1561/2200000073.

        +
        +
        +

        Vanderbei, Robert. 2014. Linear Programming : Foundations and Extensions. New York: Springer.

        +

        Wentzel, Elena S. 1988. Operations Research: A Methodological Approach. Moscow: Mir publishers.

        diff --git a/bib/bibliography.bib b/bib/bibliography.bib index 8bac017..c4ddd04 100644 --- a/bib/bibliography.bib +++ b/bib/bibliography.bib @@ -203,3 +203,88 @@ address = {Chichester, West Sussex}, isbn = {9781118443330}, } + +@book{chvatal1983_linear, + author = {Chv{\'a}tal, Va{\v{s}}ek}, + title = {Linear programming}, + year = {1983}, + publisher = {W.H. Freeman}, + address = {New York}, + isbn = {0716715872}, +} + +@book{vanderbei2014_linear, + author = {Vanderbei, Robert}, + title = {Linear programming : foundations and extensions}, + year = {2014}, + publisher = {Springer}, + address = {New York}, + isbn = {9781461476306}, +} + +@Book{dantzig1997_linear, + author = {Dantzig, George}, + title = {Linear programming 1: Introduction}, + year = 1997, + publisher = {Springer}, + url = {https://www.springer.com/gp/book/9780387948331}, + address = {New York}, + isbn = 9780387226330, +} + +@Book{dantzig2003_linear, + author = {Dantzig, George}, + title = {Linear programming 2: Theory and Extensions}, + year = 2003, + publisher = {Springer}, + url = {https://www.springer.com/gp/book/9780387986135}, + address = {New York}, + isbn = 9780387215693, +} + +@Book{bertsimas1997_introd, + author = {Bertsimas, Dimitris and Tsitsiklis, John N.}, + title = {Introduction to linear optimization}, + year = 1997, + publisher = {Athena Scientific}, + url = {http://www.athenasc.com/linoptbook.html}, + address = {Belmont, Massachusetts}, + isbn = 9781886529199, +} + +@Book{maros2003_comput, + author = {Maros, Istv{\'a}n}, + title = {Computational techniques of the simplex method}, + year = 2003, + publisher = {Kluwer Academic Publishers}, + address = {Boston}, + isbn = 9781402073328, +} + +@Book{nocedal2006_numer, + author = {Nocedal, Jorge}, + title = {Numerical optimization}, + year = 2006, + publisher = {Springer}, + url = {https://www.springer.com/gp/book/9780387303031}, + address = {New York}, + isbn = 9780387303031, +} + +@Book{boyd2004_convex, + author = {Boyd, Stephen}, + title = {Convex optimization}, + year = 2004, + publisher = {Cambridge University Press}, + address = {Cambridge, UK New York}, + isbn = 9780521833783, +} + +@Book{kochenderfer2019_algor, + author = {Kochenderfer, Mykel}, + title = {Algorithms for optimization}, + year = 2019, + publisher = {The MIT Press}, + address = {Cambridge, Massachusetts}, + isbn = 9780262039420, +} diff --git a/posts/operations-research-references.org b/posts/operations-research-references.org index b8b376b..1dd22cc 100644 --- a/posts/operations-research-references.org +++ b/posts/operations-research-references.org @@ -105,6 +105,42 @@ solvers [[solvers][below]]). ** Theory and algorithms +The basic algorithm for optimization is the [[https://en.wikipedia.org/wiki/Simplex_algorithm][simplex algorithm]], +developed by Dantzig in the 1940s to solve [[https://en.wikipedia.org/wiki/Linear_programming][linear programming]] +problems. It is the one of the main building blocks for mathematical +optimization, and is used and referenced extensively in all kinds of +approaches. As such, it is really important to understand it in +detail. There are many books on the subject, but I especially liked +cite:chvatal1983_linear (out of print, but you can find cheap used +versions on Amazon). It covers everything there is to know on the +simplex algorithms (step-by-step explanations with simple examples, +correctness and complexity analysis, computational and implementation +considerations) and to many applications. I think it is overall the +best introduction. cite:vanderbei2014_linear follows a very similar +outline, but contains more recent computational +considerations[fn:simplex_implem]. (The author also has [[http://vanderbei.princeton.edu/307/lectures.html][lecture +slides]].) + +[fn:simplex_implem] For all the details about practical +implementations of the simplex algorithm, cite:maros2003_comput is +dedicated to the computational aspects and contains everything you +will need. + + +For more books on linear programming, the two books +cite:dantzig1997_linear, cite:dantzig2003_linear are very complete, if +somewhat more mathematically advanced. cite:bertsimas1997_introd is +also a great reference, if you can find it. + +For all the other subfields, [[https://or.stackexchange.com/a/870][this great StackExchange answer]] contains +a lot of useful references, including most of the above. Of particular +note are cite:peyreComputationalOptimalTransport2019 for optimal +transport, cite:boyd2004_convex for convex optimization ([[https://web.stanford.edu/~boyd/cvxbook/][freely +available online]]), and cite:nocedal2006_numer for numerical +optimization. cite:kochenderfer2019_algor is not in the list (because +it is very recent) but is also excellent, with examples in Julia +covering nearly every kind of optimization algorithms. + ** Online courses * Solvers and computational resources <> From 24b7185ef42baf275d929bc3f7b918c62dedd05d Mon Sep 17 00:00:00 2001 From: Dimitri Lozeve Date: Wed, 27 May 2020 09:52:36 +0200 Subject: [PATCH 6/9] Add references to online courses --- _site/atom.xml | 14 ++++++++ .../posts/operations-research-references.html | 14 ++++++++ _site/rss.xml | 14 ++++++++ posts/operations-research-references.org | 35 +++++++++++++++++++ 4 files changed, 77 insertions(+) diff --git a/_site/atom.xml b/_site/atom.xml index 49b53cd..1e6eb4e 100644 --- a/_site/atom.xml +++ b/_site/atom.xml @@ -43,6 +43,20 @@

        For more books on linear programming, the two books Dantzig (1997), Dantzig (2003) are very complete, if somewhat more mathematically advanced. Bertsimas and Tsitsiklis (1997) is also a great reference, if you can find it.

        For all the other subfields, this great StackExchange answer contains a lot of useful references, including most of the above. Of particular note are Peyré and Cuturi (2019) for optimal transport, Boyd (2004) for convex optimization (freely available online), and Nocedal (2006) for numerical optimization. Kochenderfer (2019) is not in the list (because it is very recent) but is also excellent, with examples in Julia covering nearly every kind of optimization algorithms.

        Online courses

        +

        If you would like to watch video lectures, there are a few good opportunities freely available online, in particular on MIT OpenCourseWare. The list of courses at MIT is available on their webpage. I haven’t actually looked in details at the courses contentI am more comfortable reading books than watching lecture videos online. Although I liked attending classes during my studies, I do not have the same feeling in front of a video. When I read, I can re-read three times the same sentence, pause to look up something, or skim a few paragraphs. I find that the inability to do that with a video diminishes greatly my ability to concentrate.
        +
        +        , so I cannot vouch for them directly, but MIT courses are generally of excellent quality. Most courses are also taught by Bertsimas and Bertsekas, who are very famous and wrote many excellent books.

        +

        Of particular notes are:

        + +

        Another interesting course I found online is Deep Learning in Discrete Optimization, at Johns Hopkins It is taught by William Cook, who is the author of In Pursuit of the Traveling Salesman, a nice introduction to the TSP problem in a readable form.
        +
        +        . It contains an interesting overview of deep learning and integer programming, with a focus on connections, and applications to recent research areas in ML (reinforcement learning, attention, etc.).

        Solvers and computational resources

        References

        diff --git a/_site/posts/operations-research-references.html b/_site/posts/operations-research-references.html index 4a2cb9f..9ff6870 100644 --- a/_site/posts/operations-research-references.html +++ b/_site/posts/operations-research-references.html @@ -72,6 +72,20 @@

        For more books on linear programming, the two books Dantzig (1997), Dantzig (2003) are very complete, if somewhat more mathematically advanced. Bertsimas and Tsitsiklis (1997) is also a great reference, if you can find it.

        For all the other subfields, this great StackExchange answer contains a lot of useful references, including most of the above. Of particular note are Peyré and Cuturi (2019) for optimal transport, Boyd (2004) for convex optimization (freely available online), and Nocedal (2006) for numerical optimization. Kochenderfer (2019) is not in the list (because it is very recent) but is also excellent, with examples in Julia covering nearly every kind of optimization algorithms.

        Online courses

        +

        If you would like to watch video lectures, there are a few good opportunities freely available online, in particular on MIT OpenCourseWare. The list of courses at MIT is available on their webpage. I haven’t actually looked in details at the courses contentI am more comfortable reading books than watching lecture videos online. Although I liked attending classes during my studies, I do not have the same feeling in front of a video. When I read, I can re-read three times the same sentence, pause to look up something, or skim a few paragraphs. I find that the inability to do that with a video diminishes greatly my ability to concentrate.
        +
        +        , so I cannot vouch for them directly, but MIT courses are generally of excellent quality. Most courses are also taught by Bertsimas and Bertsekas, who are very famous and wrote many excellent books.

        +

        Of particular notes are:

        + +

        Another interesting course I found online is Deep Learning in Discrete Optimization, at Johns Hopkins It is taught by William Cook, who is the author of In Pursuit of the Traveling Salesman, a nice introduction to the TSP problem in a readable form.
        +
        +        . It contains an interesting overview of deep learning and integer programming, with a focus on connections, and applications to recent research areas in ML (reinforcement learning, attention, etc.).

        Solvers and computational resources

        References

        diff --git a/_site/rss.xml b/_site/rss.xml index c273d5d..a208a8c 100644 --- a/_site/rss.xml +++ b/_site/rss.xml @@ -39,6 +39,20 @@

        For more books on linear programming, the two books Dantzig (1997), Dantzig (2003) are very complete, if somewhat more mathematically advanced. Bertsimas and Tsitsiklis (1997) is also a great reference, if you can find it.

        For all the other subfields, this great StackExchange answer contains a lot of useful references, including most of the above. Of particular note are Peyré and Cuturi (2019) for optimal transport, Boyd (2004) for convex optimization (freely available online), and Nocedal (2006) for numerical optimization. Kochenderfer (2019) is not in the list (because it is very recent) but is also excellent, with examples in Julia covering nearly every kind of optimization algorithms.

        Online courses

        +

        If you would like to watch video lectures, there are a few good opportunities freely available online, in particular on MIT OpenCourseWare. The list of courses at MIT is available on their webpage. I haven’t actually looked in details at the courses contentI am more comfortable reading books than watching lecture videos online. Although I liked attending classes during my studies, I do not have the same feeling in front of a video. When I read, I can re-read three times the same sentence, pause to look up something, or skim a few paragraphs. I find that the inability to do that with a video diminishes greatly my ability to concentrate.
        +
        +        , so I cannot vouch for them directly, but MIT courses are generally of excellent quality. Most courses are also taught by Bertsimas and Bertsekas, who are very famous and wrote many excellent books.

        +

        Of particular notes are:

        + +

        Another interesting course I found online is Deep Learning in Discrete Optimization, at Johns Hopkins It is taught by William Cook, who is the author of In Pursuit of the Traveling Salesman, a nice introduction to the TSP problem in a readable form.
        +
        +        . It contains an interesting overview of deep learning and integer programming, with a focus on connections, and applications to recent research areas in ML (reinforcement learning, attention, etc.).

        Solvers and computational resources

        References

        diff --git a/posts/operations-research-references.org b/posts/operations-research-references.org index 1dd22cc..b690de8 100644 --- a/posts/operations-research-references.org +++ b/posts/operations-research-references.org @@ -143,6 +143,41 @@ covering nearly every kind of optimization algorithms. ** Online courses +If you would like to watch video lectures, there are a few good +opportunities freely available online, in particular on [[https://ocw.mit.edu/index.htm][MIT +OpenCourseWare]]. The list of courses at MIT is available [[https://orc.mit.edu/academics/course-offerings][on their +webpage]]. I haven't actually looked in details at the courses +content[fn:courses], so I cannot vouch for them directly, but MIT +courses are generally of excellent quality. Most courses are also +taught by Bertsimas and Bertsekas, who are very famous and wrote many +excellent books. + +[fn:courses] I am more comfortable reading books than watching lecture +videos online. Although I liked attending classes during my studies, I +do not have the same feeling in front of a video. When I read, I can +re-read three times the same sentence, pause to look up something, or +skim a few paragraphs. I find that the inability to do that with a +video diminishes greatly my ability to concentrate. + + +Of particular notes are: +- [[https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-251j-introduction-to-mathematical-programming-fall-2009/][Introduction to Mathematical Programming]], +- [[https://ocw.mit.edu/courses/sloan-school-of-management/15-084j-nonlinear-programming-spring-2004/][Nonlinear Optimization]], +- [[https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-253-convex-analysis-and-optimization-spring-2012/][Convex Analysis and Optimization]], +- [[https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-972-algebraic-techniques-and-semidefinite-optimization-spring-2006/][Algebraic Techniques and Semidefinite Optimization]], +- [[https://ocw.mit.edu/courses/sloan-school-of-management/15-083j-integer-programming-and-combinatorial-optimization-fall-2009/][Integer Programming and Combinatorial Optimization]]. + +Another interesting course I found online is [[https://www.ams.jhu.edu/~wcook12/dl/index.html][Deep Learning in Discrete +Optimization]], at Johns Hopkins[fn:cook]. It contains an interesting +overview of deep learning and integer programming, with a focus on +connections, and applications to recent research areas in ML +(reinforcement learning, attention, etc.). + +[fn:cook] {-} It is taught by William Cook, who is the author of [[https://press.princeton.edu/books/paperback/9780691163529/in-pursuit-of-the-traveling-salesman][/In +Pursuit of the Traveling Salesman/]], a nice introduction to the TSP +problem in a readable form. + + * Solvers and computational resources <> * References From 79eb1342e9c02098c4dac10052455775b03b3daa Mon Sep 17 00:00:00 2001 From: Dimitri Lozeve Date: Wed, 27 May 2020 10:12:00 +0200 Subject: [PATCH 7/9] Add solvers --- _site/atom.xml | 5 +++ .../posts/operations-research-references.html | 5 +++ _site/rss.xml | 5 +++ posts/operations-research-references.org | 34 +++++++++++++++++++ 4 files changed, 49 insertions(+) diff --git a/_site/atom.xml b/_site/atom.xml index 1e6eb4e..70efb25 100644 --- a/_site/atom.xml +++ b/_site/atom.xml @@ -58,6 +58,11 @@
        . It contains an interesting overview of deep learning and integer programming, with a focus on connections, and applications to recent research areas in ML (reinforcement learning, attention, etc.).

        Solvers and computational resources

        +

        When you start reading about modelling and algorithms, I recommend you try solving a few problems yourself, either by hand for small instances, or using an existing solver. It will allow you to follow the examples in books, while also practising your modelling skills. You will also get an intuition of what is difficult to model and to solve.

        +

        There are many solvers available, both free and commercial, with various capabilities. I recommend you use the fantastic JuMP library for Julia, which exposes a domain-specific language for modelling, along with interfaces to nearly all major solver packages. (Even if you don’t know Julia, this is a great and easy way to start!) If you’d rather use Python, you can use Google’s OR-Tools or PuLP for linear programming.

        +

        Regarding solvers, there is a list of solvers on JuMP’s documentation, with their capabilities and their license. Free solvers include GLPK (linear programming), Ipopt (non-linear programming), and SCIP (mixed-integer linear programming).

        +

        Commercial solvers often have better performance, and some of them propose a free academic license: MOSEK, Gurobi, and IBM CPLEX in particular all offer free academic licenses and work very well with JuMP.

        +

        Another awesome resource is the NEOS Server. It offers free computing resources for numerical optimization, including all major free and commercial solvers! You can submit jobs on it in a standard format, or interface your favourite programming language with it. The fact that such an amazing resource exists for free, for everyone is extraordinary. They also have an accompanying book, the NEOS Guide, containing many case studies and description of problem types. The taxonomy may be particularly useful.

        References

        diff --git a/_site/posts/operations-research-references.html b/_site/posts/operations-research-references.html index 9ff6870..061c091 100644 --- a/_site/posts/operations-research-references.html +++ b/_site/posts/operations-research-references.html @@ -87,6 +87,11 @@
        . It contains an interesting overview of deep learning and integer programming, with a focus on connections, and applications to recent research areas in ML (reinforcement learning, attention, etc.).

        Solvers and computational resources

        +

        When you start reading about modelling and algorithms, I recommend you try solving a few problems yourself, either by hand for small instances, or using an existing solver. It will allow you to follow the examples in books, while also practising your modelling skills. You will also get an intuition of what is difficult to model and to solve.

        +

        There are many solvers available, both free and commercial, with various capabilities. I recommend you use the fantastic JuMP library for Julia, which exposes a domain-specific language for modelling, along with interfaces to nearly all major solver packages. (Even if you don’t know Julia, this is a great and easy way to start!) If you’d rather use Python, you can use Google’s OR-Tools or PuLP for linear programming.

        +

        Regarding solvers, there is a list of solvers on JuMP’s documentation, with their capabilities and their license. Free solvers include GLPK (linear programming), Ipopt (non-linear programming), and SCIP (mixed-integer linear programming).

        +

        Commercial solvers often have better performance, and some of them propose a free academic license: MOSEK, Gurobi, and IBM CPLEX in particular all offer free academic licenses and work very well with JuMP.

        +

        Another awesome resource is the NEOS Server. It offers free computing resources for numerical optimization, including all major free and commercial solvers! You can submit jobs on it in a standard format, or interface your favourite programming language with it. The fact that such an amazing resource exists for free, for everyone is extraordinary. They also have an accompanying book, the NEOS Guide, containing many case studies and description of problem types. The taxonomy may be particularly useful.

        References

        diff --git a/_site/rss.xml b/_site/rss.xml index a208a8c..1fa5713 100644 --- a/_site/rss.xml +++ b/_site/rss.xml @@ -54,6 +54,11 @@
        . It contains an interesting overview of deep learning and integer programming, with a focus on connections, and applications to recent research areas in ML (reinforcement learning, attention, etc.).

        Solvers and computational resources

        +

        When you start reading about modelling and algorithms, I recommend you try solving a few problems yourself, either by hand for small instances, or using an existing solver. It will allow you to follow the examples in books, while also practising your modelling skills. You will also get an intuition of what is difficult to model and to solve.

        +

        There are many solvers available, both free and commercial, with various capabilities. I recommend you use the fantastic JuMP library for Julia, which exposes a domain-specific language for modelling, along with interfaces to nearly all major solver packages. (Even if you don’t know Julia, this is a great and easy way to start!) If you’d rather use Python, you can use Google’s OR-Tools or PuLP for linear programming.

        +

        Regarding solvers, there is a list of solvers on JuMP’s documentation, with their capabilities and their license. Free solvers include GLPK (linear programming), Ipopt (non-linear programming), and SCIP (mixed-integer linear programming).

        +

        Commercial solvers often have better performance, and some of them propose a free academic license: MOSEK, Gurobi, and IBM CPLEX in particular all offer free academic licenses and work very well with JuMP.

        +

        Another awesome resource is the NEOS Server. It offers free computing resources for numerical optimization, including all major free and commercial solvers! You can submit jobs on it in a standard format, or interface your favourite programming language with it. The fact that such an amazing resource exists for free, for everyone is extraordinary. They also have an accompanying book, the NEOS Guide, containing many case studies and description of problem types. The taxonomy may be particularly useful.

        References

        diff --git a/posts/operations-research-references.org b/posts/operations-research-references.org index b690de8..07507bb 100644 --- a/posts/operations-research-references.org +++ b/posts/operations-research-references.org @@ -180,4 +180,38 @@ problem in a readable form. * Solvers and computational resources <> +When you start reading about modelling and algorithms, I recommend you +try solving a few problems yourself, either by hand for small +instances, or using an existing solver. It will allow you to follow +the examples in books, while also practising your modelling +skills. You will also get an intuition of what is difficult to model +and to solve. + +There are many solvers available, both free and commercial, with +various capabilities. I recommend you use the fantastic [[https://github.com/JuliaOpt/JuMP.jl][JuMP]] library +for Julia, which exposes a domain-specific language for modelling, +along with interfaces to nearly all major solver packages. (Even if +you don't know Julia, this is a great and easy way to start!) If you'd +rather use Python, you can use Google's [[https://developers.google.com/optimization/introduction/python][OR-Tools]] or [[https://github.com/coin-or/pulp][PuLP]] for linear +programming. + +Regarding solvers, there is a [[http://www.juliaopt.org/JuMP.jl/stable/installation/#Getting-Solvers-1][list of solvers]] on JuMP's documentation, +with their capabilities and their license. Free solvers include [[https://www.gnu.org/software/glpk/][GLPK]] +(linear programming), [[https://github.com/coin-or/Ipopt][Ipopt]] (non-linear programming), and [[https://scip.zib.de/][SCIP]] +(mixed-integer linear programming). + +Commercial solvers often have better performance, and some of them +propose a free academic license: [[https://www.mosek.com/][MOSEK]], [[https://www.gurobi.com/][Gurobi]], and [[https://www.ibm.com/analytics/cplex-optimizer][IBM CPLEX]] in +particular all offer free academic licenses and work very well with +JuMP. + +Another awesome resource is the [[https://neos-server.org/neos/][NEOS Server]]. It offers free computing +resources for numerical optimization, including all major free and +commercial solvers! You can submit jobs on it in a standard format, or +interface your favourite programming language with it. The fact that +such an amazing resource exists for free, for everyone is +extraordinary. They also have an accompanying book, the [[https://neos-guide.org/][NEOS Guide]], +containing many case studies and description of problem types. The +[[https://neos-guide.org/content/optimization-taxonomy][taxonomy]] may be particularly useful. + * References From 0a8a606f2643b0a59bdf046f9f02542daa1c9af5 Mon Sep 17 00:00:00 2001 From: Dimitri Lozeve Date: Wed, 27 May 2020 10:33:45 +0200 Subject: [PATCH 8/9] Final update --- _site/archive.html | 2 +- _site/atom.xml | 18 +++++----- _site/index.html | 2 +- .../posts/operations-research-references.html | 18 +++++----- _site/rss.xml | 16 +++++---- posts/operations-research-references.org | 34 +++++++++++-------- 6 files changed, 51 insertions(+), 39 deletions(-) diff --git a/_site/archive.html b/_site/archive.html index 99dc5fb..f3d8a89 100644 --- a/_site/archive.html +++ b/_site/archive.html @@ -48,7 +48,7 @@
        • - Operations Research and Optimisation: where to start? - May 26, 2020 + Operations Research and Optimization: where to start? - May 27, 2020
        • diff --git a/_site/atom.xml b/_site/atom.xml index 70efb25..e93b429 100644 --- a/_site/atom.xml +++ b/_site/atom.xml @@ -8,20 +8,20 @@ Dimitri Lozeve dimitri+web@lozeve.com - 2020-05-26T00:00:00Z + 2020-05-27T00:00:00Z - Operations Research and Optimisation: where to start? + Operations Research and Optimization: where to start? https://www.lozeve.com/posts/operations-research-references.html - 2020-05-26T00:00:00Z - 2020-05-26T00:00:00Z + 2020-05-27T00:00:00Z + 2020-05-27T00:00:00Z
          -

          Operations research (OR) is a vast area comprising a lot of theory, different branches of mathematics, and too many applications to count. In this post, I will try to explain why I find it so fascinating, but also why it can be a little disconcerting to explore at first. Then I will try to ease the newcomer’s path in this rich area, by suggesting a very rough “map” of the field and a few references to get started.

          -

          Keep in mind that although I studied it during my graduate studies, this is not my primary area of expertise (I’m a data scientist by trade), and I definitely don’t pretend to know everything in OR. This is a field too vast for any single person to understand in its entirety, and I talk mostly from a “amateur mathematician and computer scientist” standpoint.

          +

          Operations research (OR) is a vast area comprising a lot of theory, different branches of mathematics, and too many applications to count. In this post, I will try to explain why it can be a little disconcerting to explore at first, and how to start investigating the topic with a few references to get started.

          +

          Keep in mind that although I studied it during my graduate studies, this is not my primary area of expertise (I’m a data scientist by trade), and I definitely don’t pretend to know everything in OR. This is a field too vast for any single person to understand in its entirety, and I talk mostly from an “amateur mathematician and computer scientist” standpoint.

          Why is it hard to approach?

          Operations research can be difficult to approach, since there are many references and subfields. Compared to machine learning for instance, OR has a slightly longer history (going back to the 17th century, for example with Monge and the optimal transport problem) For a very nice introduction (in French) to optimal transport, see these blog posts by Gabriel Peyré, on the CNRS maths blog: Part 1 and Part 2. See also the resources on optimaltransport.github.io (in English).

          @@ -33,8 +33,8 @@

          For an overall introduction, I recommend Wentzel (1988). It is an old book, published by Mir Publications, a Soviet publisher which published many excellent scientific textbooks Mir also published Physics for Everyone by Lev Landau and Alexander Kitaigorodsky, a three-volume introduction to physics that is really accessible. Together with Feynman’s famous lectures, I read them (in French) when I was a kid, and it was the best introduction I could possibly have to the subject.

          . It is out of print, but it is available on Archive.org. The book is quite old, but everything presented is still extremely relevant today. It requires absolutely no background, and covers everything: a general introduction to the field, linear programming, dynamic programming, Markov processes and queues, Monte Carlo methods, and game theory. Even if you already know some of these topics, the presentations is so clear that it is a pleasure to read! (In particular, it is one of the best presentations of dynamic programming that I have ever read. The explanation of the simplex algorithm is also excellent.)

          -

          If you are interested in optimization, the first thing you have to learn is modelling, i.e. transforming your problem (described in natural language, often from a particular industrial application) into a mathematical programme. The mathematical programme is the structure on which you will be able to apply an algorithm to find an optimal solution. Even if (like me) you are initially more interested by the algorithmic side of things, learning to create models will shed a lot of light on the overall process, and will give you more insight in general on the reasoning behind algorithms.

          -

          The best book I have read on the subject is Williams (2013). It contains a lot of concrete, step-by-step examples on concrete applications, in a multitude of domains, and remains very easy to read and to follow. It covers nearly every type of problem, so it is very useful as a reference. When you encounter a concrete problem in real life afterwards, you will know how to construct an appropriate model, and in the process you will often identify a common type of problem. The book then gives plenty of advice on how to best approach each type of problem. Finally, it is also a great resource to build a “mental map” of the field, avoiding to get lost in the jungle of linear, stochastic, mixed integer, quadratic, and other network problems.

          +

          If you are interested in optimization, the first thing you have to learn is modelling, i.e. transforming your problem (described in natural language, often from a particular industrial application) into a mathematical programme. The mathematical programme is the structure on which you will be able to apply an algorithm to find an optimal solution. Even if (like me) you are initially more interested in the algorithmic side of things, learning to create models will shed a lot of light on the overall process, and will give you more insight in general on the reasoning behind algorithms.

          +

          The best book I have read on the subject is Williams (2013). It contains a lot of concrete, step-by-step examples on concrete applications, in a multitude of domains, and remains very easy to read and to follow. It covers nearly every type of problem, so it is very useful as a reference. When you encounter a concrete problem in real life afterwards, you will know how to construct an appropriate model, and in the process you will often identify a common type of problem. The book then gives plenty of advice on how to approach each type of problem. Finally, it is also a great resource to build a “mental map” of the field, avoiding getting lost in the jungle of linear, stochastic, mixed integer, quadratic, and other network problems.

          Another interesting resource is the freely available MOSEK Modeling Cookbook, covering many types of problems, with more mathematical details than in Williams (2013). It is built for people wanting to use the commercial MOSEK solver, so it could be useful if you plan to use a solver package like this one (more details on solvers below).

          Theory and algorithms

          The basic algorithm for optimization is the simplex algorithm, developed by Dantzig in the 1940s to solve linear programming problems. It is the one of the main building blocks for mathematical optimization, and is used and referenced extensively in all kinds of approaches. As such, it is really important to understand it in detail. There are many books on the subject, but I especially liked Chvátal (1983) (out of print, but you can find cheap used versions on Amazon). It covers everything there is to know on the simplex algorithms (step-by-step explanations with simple examples, correctness and complexity analysis, computational and implementation considerations) and to many applications. I think it is overall the best introduction. Vanderbei (2014) follows a very similar outline, but contains more recent computational considerationsFor all the details about practical implementations of the simplex algorithm, Maros (2003) is dedicated to the computational aspects and contains everything you will need.
          @@ -63,6 +63,8 @@

          Regarding solvers, there is a list of solvers on JuMP’s documentation, with their capabilities and their license. Free solvers include GLPK (linear programming), Ipopt (non-linear programming), and SCIP (mixed-integer linear programming).

          Commercial solvers often have better performance, and some of them propose a free academic license: MOSEK, Gurobi, and IBM CPLEX in particular all offer free academic licenses and work very well with JuMP.

          Another awesome resource is the NEOS Server. It offers free computing resources for numerical optimization, including all major free and commercial solvers! You can submit jobs on it in a standard format, or interface your favourite programming language with it. The fact that such an amazing resource exists for free, for everyone is extraordinary. They also have an accompanying book, the NEOS Guide, containing many case studies and description of problem types. The taxonomy may be particularly useful.

          +

          Conclusion

          +

          Operations research is a fascinating topic, and it has an abundant literature that makes it very easy to dive into the subject. If you are interested in algorithms, modelling for practical applications, or just wish to understand more, I hope to have given you the first steps to follow, start reading and experimenting.

          References

          diff --git a/_site/index.html b/_site/index.html index 6250f24..6ed178d 100644 --- a/_site/index.html +++ b/_site/index.html @@ -71,7 +71,7 @@ public key: RWQ6uexORp8f7USHA7nX9lFfltaCA9x6aBV06MvgiGjUt6BVf6McyD26
          • - Operations Research and Optimisation: where to start? - May 26, 2020 + Operations Research and Optimization: where to start? - May 27, 2020
          • diff --git a/_site/posts/operations-research-references.html b/_site/posts/operations-research-references.html index 061c091..03835b0 100644 --- a/_site/posts/operations-research-references.html +++ b/_site/posts/operations-research-references.html @@ -4,9 +4,9 @@ - + - Dimitri Lozeve - Operations Research and Optimisation: where to start? + Dimitri Lozeve - Operations Research and Optimization: where to start? @@ -33,10 +33,10 @@ Contact -

            Operations Research and Optimisation: where to start?

            +

            Operations Research and Optimization: where to start?

            -

            May 26, 2020

            +

            May 27, 2020

            @@ -49,8 +49,8 @@
          -

          Operations research (OR) is a vast area comprising a lot of theory, different branches of mathematics, and too many applications to count. In this post, I will try to explain why I find it so fascinating, but also why it can be a little disconcerting to explore at first. Then I will try to ease the newcomer’s path in this rich area, by suggesting a very rough “map” of the field and a few references to get started.

          -

          Keep in mind that although I studied it during my graduate studies, this is not my primary area of expertise (I’m a data scientist by trade), and I definitely don’t pretend to know everything in OR. This is a field too vast for any single person to understand in its entirety, and I talk mostly from a “amateur mathematician and computer scientist” standpoint.

          +

          Operations research (OR) is a vast area comprising a lot of theory, different branches of mathematics, and too many applications to count. In this post, I will try to explain why it can be a little disconcerting to explore at first, and how to start investigating the topic with a few references to get started.

          +

          Keep in mind that although I studied it during my graduate studies, this is not my primary area of expertise (I’m a data scientist by trade), and I definitely don’t pretend to know everything in OR. This is a field too vast for any single person to understand in its entirety, and I talk mostly from an “amateur mathematician and computer scientist” standpoint.

          Why is it hard to approach?

          Operations research can be difficult to approach, since there are many references and subfields. Compared to machine learning for instance, OR has a slightly longer history (going back to the 17th century, for example with Monge and the optimal transport problem) For a very nice introduction (in French) to optimal transport, see these blog posts by Gabriel Peyré, on the CNRS maths blog: Part 1 and Part 2. See also the resources on optimaltransport.github.io (in English).

          @@ -62,8 +62,8 @@

          For an overall introduction, I recommend Wentzel (1988). It is an old book, published by Mir Publications, a Soviet publisher which published many excellent scientific textbooks Mir also published Physics for Everyone by Lev Landau and Alexander Kitaigorodsky, a three-volume introduction to physics that is really accessible. Together with Feynman’s famous lectures, I read them (in French) when I was a kid, and it was the best introduction I could possibly have to the subject.

          . It is out of print, but it is available on Archive.org. The book is quite old, but everything presented is still extremely relevant today. It requires absolutely no background, and covers everything: a general introduction to the field, linear programming, dynamic programming, Markov processes and queues, Monte Carlo methods, and game theory. Even if you already know some of these topics, the presentations is so clear that it is a pleasure to read! (In particular, it is one of the best presentations of dynamic programming that I have ever read. The explanation of the simplex algorithm is also excellent.)

          -

          If you are interested in optimization, the first thing you have to learn is modelling, i.e. transforming your problem (described in natural language, often from a particular industrial application) into a mathematical programme. The mathematical programme is the structure on which you will be able to apply an algorithm to find an optimal solution. Even if (like me) you are initially more interested by the algorithmic side of things, learning to create models will shed a lot of light on the overall process, and will give you more insight in general on the reasoning behind algorithms.

          -

          The best book I have read on the subject is Williams (2013). It contains a lot of concrete, step-by-step examples on concrete applications, in a multitude of domains, and remains very easy to read and to follow. It covers nearly every type of problem, so it is very useful as a reference. When you encounter a concrete problem in real life afterwards, you will know how to construct an appropriate model, and in the process you will often identify a common type of problem. The book then gives plenty of advice on how to best approach each type of problem. Finally, it is also a great resource to build a “mental map” of the field, avoiding to get lost in the jungle of linear, stochastic, mixed integer, quadratic, and other network problems.

          +

          If you are interested in optimization, the first thing you have to learn is modelling, i.e. transforming your problem (described in natural language, often from a particular industrial application) into a mathematical programme. The mathematical programme is the structure on which you will be able to apply an algorithm to find an optimal solution. Even if (like me) you are initially more interested in the algorithmic side of things, learning to create models will shed a lot of light on the overall process, and will give you more insight in general on the reasoning behind algorithms.

          +

          The best book I have read on the subject is Williams (2013). It contains a lot of concrete, step-by-step examples on concrete applications, in a multitude of domains, and remains very easy to read and to follow. It covers nearly every type of problem, so it is very useful as a reference. When you encounter a concrete problem in real life afterwards, you will know how to construct an appropriate model, and in the process you will often identify a common type of problem. The book then gives plenty of advice on how to approach each type of problem. Finally, it is also a great resource to build a “mental map” of the field, avoiding getting lost in the jungle of linear, stochastic, mixed integer, quadratic, and other network problems.

          Another interesting resource is the freely available MOSEK Modeling Cookbook, covering many types of problems, with more mathematical details than in Williams (2013). It is built for people wanting to use the commercial MOSEK solver, so it could be useful if you plan to use a solver package like this one (more details on solvers below).

          Theory and algorithms

          The basic algorithm for optimization is the simplex algorithm, developed by Dantzig in the 1940s to solve linear programming problems. It is the one of the main building blocks for mathematical optimization, and is used and referenced extensively in all kinds of approaches. As such, it is really important to understand it in detail. There are many books on the subject, but I especially liked Chvátal (1983) (out of print, but you can find cheap used versions on Amazon). It covers everything there is to know on the simplex algorithms (step-by-step explanations with simple examples, correctness and complexity analysis, computational and implementation considerations) and to many applications. I think it is overall the best introduction. Vanderbei (2014) follows a very similar outline, but contains more recent computational considerationsFor all the details about practical implementations of the simplex algorithm, Maros (2003) is dedicated to the computational aspects and contains everything you will need.
          @@ -92,6 +92,8 @@

          Regarding solvers, there is a list of solvers on JuMP’s documentation, with their capabilities and their license. Free solvers include GLPK (linear programming), Ipopt (non-linear programming), and SCIP (mixed-integer linear programming).

          Commercial solvers often have better performance, and some of them propose a free academic license: MOSEK, Gurobi, and IBM CPLEX in particular all offer free academic licenses and work very well with JuMP.

          Another awesome resource is the NEOS Server. It offers free computing resources for numerical optimization, including all major free and commercial solvers! You can submit jobs on it in a standard format, or interface your favourite programming language with it. The fact that such an amazing resource exists for free, for everyone is extraordinary. They also have an accompanying book, the NEOS Guide, containing many case studies and description of problem types. The taxonomy may be particularly useful.

          +

          Conclusion

          +

          Operations research is a fascinating topic, and it has an abundant literature that makes it very easy to dive into the subject. If you are interested in algorithms, modelling for practical applications, or just wish to understand more, I hope to have given you the first steps to follow, start reading and experimenting.

          References

          diff --git a/_site/rss.xml b/_site/rss.xml index 1fa5713..a90e537 100644 --- a/_site/rss.xml +++ b/_site/rss.xml @@ -7,17 +7,17 @@ - Tue, 26 May 2020 00:00:00 UT + Wed, 27 May 2020 00:00:00 UT - Operations Research and Optimisation: where to start? + Operations Research and Optimization: where to start? https://www.lozeve.com/posts/operations-research-references.html
          -

          Operations research (OR) is a vast area comprising a lot of theory, different branches of mathematics, and too many applications to count. In this post, I will try to explain why I find it so fascinating, but also why it can be a little disconcerting to explore at first. Then I will try to ease the newcomer’s path in this rich area, by suggesting a very rough “map” of the field and a few references to get started.

          -

          Keep in mind that although I studied it during my graduate studies, this is not my primary area of expertise (I’m a data scientist by trade), and I definitely don’t pretend to know everything in OR. This is a field too vast for any single person to understand in its entirety, and I talk mostly from a “amateur mathematician and computer scientist” standpoint.

          +

          Operations research (OR) is a vast area comprising a lot of theory, different branches of mathematics, and too many applications to count. In this post, I will try to explain why it can be a little disconcerting to explore at first, and how to start investigating the topic with a few references to get started.

          +

          Keep in mind that although I studied it during my graduate studies, this is not my primary area of expertise (I’m a data scientist by trade), and I definitely don’t pretend to know everything in OR. This is a field too vast for any single person to understand in its entirety, and I talk mostly from an “amateur mathematician and computer scientist” standpoint.

          Why is it hard to approach?

          Operations research can be difficult to approach, since there are many references and subfields. Compared to machine learning for instance, OR has a slightly longer history (going back to the 17th century, for example with Monge and the optimal transport problem) For a very nice introduction (in French) to optimal transport, see these blog posts by Gabriel Peyré, on the CNRS maths blog: Part 1 and Part 2. See also the resources on optimaltransport.github.io (in English).

          @@ -29,8 +29,8 @@

          For an overall introduction, I recommend Wentzel (1988). It is an old book, published by Mir Publications, a Soviet publisher which published many excellent scientific textbooks Mir also published Physics for Everyone by Lev Landau and Alexander Kitaigorodsky, a three-volume introduction to physics that is really accessible. Together with Feynman’s famous lectures, I read them (in French) when I was a kid, and it was the best introduction I could possibly have to the subject.

          . It is out of print, but it is available on Archive.org. The book is quite old, but everything presented is still extremely relevant today. It requires absolutely no background, and covers everything: a general introduction to the field, linear programming, dynamic programming, Markov processes and queues, Monte Carlo methods, and game theory. Even if you already know some of these topics, the presentations is so clear that it is a pleasure to read! (In particular, it is one of the best presentations of dynamic programming that I have ever read. The explanation of the simplex algorithm is also excellent.)

          -

          If you are interested in optimization, the first thing you have to learn is modelling, i.e. transforming your problem (described in natural language, often from a particular industrial application) into a mathematical programme. The mathematical programme is the structure on which you will be able to apply an algorithm to find an optimal solution. Even if (like me) you are initially more interested by the algorithmic side of things, learning to create models will shed a lot of light on the overall process, and will give you more insight in general on the reasoning behind algorithms.

          -

          The best book I have read on the subject is Williams (2013). It contains a lot of concrete, step-by-step examples on concrete applications, in a multitude of domains, and remains very easy to read and to follow. It covers nearly every type of problem, so it is very useful as a reference. When you encounter a concrete problem in real life afterwards, you will know how to construct an appropriate model, and in the process you will often identify a common type of problem. The book then gives plenty of advice on how to best approach each type of problem. Finally, it is also a great resource to build a “mental map” of the field, avoiding to get lost in the jungle of linear, stochastic, mixed integer, quadratic, and other network problems.

          +

          If you are interested in optimization, the first thing you have to learn is modelling, i.e. transforming your problem (described in natural language, often from a particular industrial application) into a mathematical programme. The mathematical programme is the structure on which you will be able to apply an algorithm to find an optimal solution. Even if (like me) you are initially more interested in the algorithmic side of things, learning to create models will shed a lot of light on the overall process, and will give you more insight in general on the reasoning behind algorithms.

          +

          The best book I have read on the subject is Williams (2013). It contains a lot of concrete, step-by-step examples on concrete applications, in a multitude of domains, and remains very easy to read and to follow. It covers nearly every type of problem, so it is very useful as a reference. When you encounter a concrete problem in real life afterwards, you will know how to construct an appropriate model, and in the process you will often identify a common type of problem. The book then gives plenty of advice on how to approach each type of problem. Finally, it is also a great resource to build a “mental map” of the field, avoiding getting lost in the jungle of linear, stochastic, mixed integer, quadratic, and other network problems.

          Another interesting resource is the freely available MOSEK Modeling Cookbook, covering many types of problems, with more mathematical details than in Williams (2013). It is built for people wanting to use the commercial MOSEK solver, so it could be useful if you plan to use a solver package like this one (more details on solvers below).

          Theory and algorithms

          The basic algorithm for optimization is the simplex algorithm, developed by Dantzig in the 1940s to solve linear programming problems. It is the one of the main building blocks for mathematical optimization, and is used and referenced extensively in all kinds of approaches. As such, it is really important to understand it in detail. There are many books on the subject, but I especially liked Chvátal (1983) (out of print, but you can find cheap used versions on Amazon). It covers everything there is to know on the simplex algorithms (step-by-step explanations with simple examples, correctness and complexity analysis, computational and implementation considerations) and to many applications. I think it is overall the best introduction. Vanderbei (2014) follows a very similar outline, but contains more recent computational considerationsFor all the details about practical implementations of the simplex algorithm, Maros (2003) is dedicated to the computational aspects and contains everything you will need.
          @@ -59,6 +59,8 @@

          Regarding solvers, there is a list of solvers on JuMP’s documentation, with their capabilities and their license. Free solvers include GLPK (linear programming), Ipopt (non-linear programming), and SCIP (mixed-integer linear programming).

          Commercial solvers often have better performance, and some of them propose a free academic license: MOSEK, Gurobi, and IBM CPLEX in particular all offer free academic licenses and work very well with JuMP.

          Another awesome resource is the NEOS Server. It offers free computing resources for numerical optimization, including all major free and commercial solvers! You can submit jobs on it in a standard format, or interface your favourite programming language with it. The fact that such an amazing resource exists for free, for everyone is extraordinary. They also have an accompanying book, the NEOS Guide, containing many case studies and description of problem types. The taxonomy may be particularly useful.

          +

          Conclusion

          +

          Operations research is a fascinating topic, and it has an abundant literature that makes it very easy to dive into the subject. If you are interested in algorithms, modelling for practical applications, or just wish to understand more, I hope to have given you the first steps to follow, start reading and experimenting.

          References

          @@ -101,7 +103,7 @@
          ]]>           - Tue, 26 May 2020 00:00:00 UT + Wed, 27 May 2020 00:00:00 UT https://www.lozeve.com/posts/operations-research-references.html Dimitri Lozeve           diff --git a/posts/operations-research-references.org b/posts/operations-research-references.org index 07507bb..3bcb33b 100644 --- a/posts/operations-research-references.org +++ b/posts/operations-research-references.org @@ -1,22 +1,20 @@ --- -title: "Operations Research and Optimisation: where to start?" -date: 2020-05-26 +title: "Operations Research and Optimization: where to start?" +date: 2020-05-27 --- [[https://en.wikipedia.org/wiki/Operations_research][Operations research]] (OR) is a vast area comprising a lot of theory, different branches of mathematics, and too many applications to -count. In this post, I will try to explain why I find it so -fascinating, but also why it can be a little disconcerting to explore -at first. Then I will try to ease the newcomer's path in this rich -area, by suggesting a very rough "map" of the field and a few -references to get started. +count. In this post, I will try to explain why it can be a little +disconcerting to explore at first, and how to start investigating the +topic with a few references to get started. Keep in mind that although I studied it during my graduate studies, this is not my primary area of expertise (I'm a data scientist by trade), and I definitely don't pretend to know everything in OR. This is a field too vast for any single person to understand in its -entirety, and I talk mostly from a "amateur mathematician and computer -scientist" standpoint. +entirety, and I talk mostly from an "amateur mathematician and +computer scientist" standpoint. * Why is it hard to approach? @@ -78,7 +76,7 @@ learn is modelling, i.e. transforming your problem (described in natural language, often from a particular industrial application) into a mathematical programme. The mathematical programme is the structure on which you will be able to apply an algorithm to find an optimal -solution. Even if (like me) you are initially more interested by the +solution. Even if (like me) you are initially more interested in the algorithmic side of things, learning to create models will shed a lot of light on the overall process, and will give you more insight in general on the reasoning behind algorithms. @@ -91,10 +89,10 @@ of problem, so it is very useful as a reference. When you encounter a concrete problem in real life afterwards, you will know how to construct an appropriate model, and in the process you will often identify a common type of problem. The book then gives plenty of -advice on how to best approach each type of problem. Finally, it is -also a great resource to build a "mental map" of the field, avoiding -to get lost in the jungle of linear, stochastic, mixed integer, -quadratic, and other network problems. +advice on how to approach each type of problem. Finally, it is also a +great resource to build a "mental map" of the field, avoiding getting +lost in the jungle of linear, stochastic, mixed integer, quadratic, +and other network problems. Another interesting resource is the freely available [[https://docs.mosek.com/modeling-cookbook/index.html][MOSEK Modeling Cookbook]], covering many types of problems, with more mathematical @@ -214,4 +212,12 @@ extraordinary. They also have an accompanying book, the [[https://neos-guide.org containing many case studies and description of problem types. The [[https://neos-guide.org/content/optimization-taxonomy][taxonomy]] may be particularly useful. +* Conclusion + +Operations research is a fascinating topic, and it has an abundant +literature that makes it very easy to dive into the subject. If you +are interested in algorithms, modelling for practical applications, or +just wish to understand more, I hope to have given you the first steps +to follow, start reading and experimenting. + * References From 5b815f5a3cade9140e0fccbfe8caf085511b1a9f Mon Sep 17 00:00:00 2001 From: Dimitri Lozeve Date: Wed, 27 May 2020 10:57:54 +0200 Subject: [PATCH 9/9] Add images --- _site/atom.xml | 30 ++++++-- _site/images/or_references/jump.svg | 1 + _site/images/or_references/kochenderfer.jpg | Bin 0 -> 55180 bytes .../or_references/kochenderfer_small.jpg | Bin 0 -> 55180 bytes _site/images/or_references/wentzel.jpg | Bin 0 -> 110180 bytes _site/images/or_references/wentzel_small.jpg | Bin 0 -> 110180 bytes _site/images/or_references/williams.jpg | Bin 0 -> 53772 bytes _site/images/or_references/williams_small.jpg | Bin 0 -> 53772 bytes .../posts/operations-research-references.html | 30 ++++++-- _site/rss.xml | 30 ++++++-- images/or_references/jump.svg | 1 + images/or_references/kochenderfer.jpg | Bin 0 -> 55180 bytes images/or_references/wentzel.jpg | Bin 0 -> 110180 bytes images/or_references/williams.jpg | Bin 0 -> 53772 bytes posts/operations-research-references.org | 64 ++++++++++++------ 15 files changed, 113 insertions(+), 43 deletions(-) create mode 100644 _site/images/or_references/jump.svg create mode 100644 _site/images/or_references/kochenderfer.jpg create mode 100644 _site/images/or_references/kochenderfer_small.jpg create mode 100644 _site/images/or_references/wentzel.jpg create mode 100644 _site/images/or_references/wentzel_small.jpg create mode 100644 _site/images/or_references/williams.jpg create mode 100644 _site/images/or_references/williams_small.jpg create mode 100644 images/or_references/jump.svg create mode 100644 images/or_references/kochenderfer.jpg create mode 100644 images/or_references/wentzel.jpg create mode 100644 images/or_references/williams.jpg diff --git a/_site/atom.xml b/_site/atom.xml index e93b429..f3b73d6 100644 --- a/_site/atom.xml +++ b/_site/atom.xml @@ -32,18 +32,30 @@

          Introduction and modelling

          For an overall introduction, I recommend Wentzel (1988). It is an old book, published by Mir Publications, a Soviet publisher which published many excellent scientific textbooks Mir also published Physics for Everyone by Lev Landau and Alexander Kitaigorodsky, a three-volume introduction to physics that is really accessible. Together with Feynman’s famous lectures, I read them (in French) when I was a kid, and it was the best introduction I could possibly have to the subject.

          -          . It is out of print, but it is available on Archive.org. The book is quite old, but everything presented is still extremely relevant today. It requires absolutely no background, and covers everything: a general introduction to the field, linear programming, dynamic programming, Markov processes and queues, Monte Carlo methods, and game theory. Even if you already know some of these topics, the presentations is so clear that it is a pleasure to read! (In particular, it is one of the best presentations of dynamic programming that I have ever read. The explanation of the simplex algorithm is also excellent.)

          +. It is out of print, but it is available on Archive.org
          +
          +
          +
          +          . The book is quite old, but everything presented is still extremely relevant today. It requires absolutely no background, and covers everything: a general introduction to the field, linear programming, dynamic programming, Markov processes and queues, Monte Carlo methods, and game theory. Even if you already know some of these topics, the presentations is so clear that it is a pleasure to read! (In particular, it is one of the best presentations of dynamic programming that I have ever read. The explanation of the simplex algorithm is also excellent.)

          If you are interested in optimization, the first thing you have to learn is modelling, i.e. transforming your problem (described in natural language, often from a particular industrial application) into a mathematical programme. The mathematical programme is the structure on which you will be able to apply an algorithm to find an optimal solution. Even if (like me) you are initially more interested in the algorithmic side of things, learning to create models will shed a lot of light on the overall process, and will give you more insight in general on the reasoning behind algorithms.

          -

          The best book I have read on the subject is Williams (2013). It contains a lot of concrete, step-by-step examples on concrete applications, in a multitude of domains, and remains very easy to read and to follow. It covers nearly every type of problem, so it is very useful as a reference. When you encounter a concrete problem in real life afterwards, you will know how to construct an appropriate model, and in the process you will often identify a common type of problem. The book then gives plenty of advice on how to approach each type of problem. Finally, it is also a great resource to build a “mental map” of the field, avoiding getting lost in the jungle of linear, stochastic, mixed integer, quadratic, and other network problems.

          +

          The best book I have read on the subject is Williams (2013)
          +
          +
          +
          +          . It contains a lot of concrete, step-by-step examples on concrete applications, in a multitude of domains, and remains very easy to read and to follow. It covers nearly every type of problem, so it is very useful as a reference. When you encounter a concrete problem in real life afterwards, you will know how to construct an appropriate model, and in the process you will often identify a common type of problem. The book then gives plenty of advice on how to approach each type of problem. Finally, it is also a great resource to build a “mental map” of the field, avoiding getting lost in the jungle of linear, stochastic, mixed integer, quadratic, and other network problems.

          Another interesting resource is the freely available MOSEK Modeling Cookbook, covering many types of problems, with more mathematical details than in Williams (2013). It is built for people wanting to use the commercial MOSEK solver, so it could be useful if you plan to use a solver package like this one (more details on solvers below).

          Theory and algorithms

          -

          The basic algorithm for optimization is the simplex algorithm, developed by Dantzig in the 1940s to solve linear programming problems. It is the one of the main building blocks for mathematical optimization, and is used and referenced extensively in all kinds of approaches. As such, it is really important to understand it in detail. There are many books on the subject, but I especially liked Chvátal (1983) (out of print, but you can find cheap used versions on Amazon). It covers everything there is to know on the simplex algorithms (step-by-step explanations with simple examples, correctness and complexity analysis, computational and implementation considerations) and to many applications. I think it is overall the best introduction. Vanderbei (2014) follows a very similar outline, but contains more recent computational considerationsFor all the details about practical implementations of the simplex algorithm, Maros (2003) is dedicated to the computational aspects and contains everything you will need.
          +

          The basic algorithm for optimization is the simplex algorithm, developed by Dantzig in the 1940s to solve linear programming problems. It is the one of the main building blocks for mathematical optimization, and is used and referenced extensively in all kinds of approaches. As such, it is really important to understand it in detail. There are many books on the subject, but I especially liked Chvátal (1983) (out of print, but you can find cheap used versions on Amazon). It covers everything there is to know on the simplex algorithms (step-by-step explanations with simple examples, correctness and complexity analysis, computational and implementation considerations) and to many applications. I think it is overall the best introduction. Vanderbei (2014) follows a very similar outline, but contains more recent computational considerationsFor all the details about practical implementations of the simplex algorithm, Maros (2003) is dedicated to the computational aspects and contains everything you will need.

          . (The author also has lecture slides.)

          For more books on linear programming, the two books Dantzig (1997), Dantzig (2003) are very complete, if somewhat more mathematically advanced. Bertsimas and Tsitsiklis (1997) is also a great reference, if you can find it.

          -

          For all the other subfields, this great StackExchange answer contains a lot of useful references, including most of the above. Of particular note are Peyré and Cuturi (2019) for optimal transport, Boyd (2004) for convex optimization (freely available online), and Nocedal (2006) for numerical optimization. Kochenderfer (2019) is not in the list (because it is very recent) but is also excellent, with examples in Julia covering nearly every kind of optimization algorithms.

          +

          For all the other subfields, this great StackExchange answer contains a lot of useful references, including most of the above. Of particular note are Peyré and Cuturi (2019) for optimal transport, Boyd (2004) for convex optimization (freely available online), and Nocedal (2006) for numerical optimization. Kochenderfer (2019)
          +
          +
          +
          +           is not in the list (because it is very recent) but is also excellent, with examples in Julia covering nearly every kind of optimization algorithms.

          Online courses

          -

          If you would like to watch video lectures, there are a few good opportunities freely available online, in particular on MIT OpenCourseWare. The list of courses at MIT is available on their webpage. I haven’t actually looked in details at the courses contentI am more comfortable reading books than watching lecture videos online. Although I liked attending classes during my studies, I do not have the same feeling in front of a video. When I read, I can re-read three times the same sentence, pause to look up something, or skim a few paragraphs. I find that the inability to do that with a video diminishes greatly my ability to concentrate.
          +

          If you would like to watch video lectures, there are a few good opportunities freely available online, in particular on MIT OpenCourseWare. The list of courses at MIT is available on their webpage. I haven’t actually looked in details at the courses contentI am more comfortable reading books than watching lecture videos online. Although I liked attending classes during my studies, I do not have the same feeling in front of a video. When I read, I can re-read three times the same sentence, pause to look up something, or skim a few paragraphs. I find that the inability to do that with a video diminishes greatly my ability to concentrate.

          , so I cannot vouch for them directly, but MIT courses are generally of excellent quality. Most courses are also taught by Bertsimas and Bertsekas, who are very famous and wrote many excellent books.

          Of particular notes are:

          @@ -54,12 +66,16 @@
        • Algebraic Techniques and Semidefinite Optimization,
        • Integer Programming and Combinatorial Optimization.
        -

        Another interesting course I found online is Deep Learning in Discrete Optimization, at Johns Hopkins It is taught by William Cook, who is the author of In Pursuit of the Traveling Salesman, a nice introduction to the TSP problem in a readable form.
        +

        Another interesting course I found online is Deep Learning in Discrete Optimization, at Johns Hopkins It is taught by William Cook, who is the author of In Pursuit of the Traveling Salesman, a nice introduction to the TSP problem in a readable form.

        . It contains an interesting overview of deep learning and integer programming, with a focus on connections, and applications to recent research areas in ML (reinforcement learning, attention, etc.).

        Solvers and computational resources

        When you start reading about modelling and algorithms, I recommend you try solving a few problems yourself, either by hand for small instances, or using an existing solver. It will allow you to follow the examples in books, while also practising your modelling skills. You will also get an intuition of what is difficult to model and to solve.

        -

        There are many solvers available, both free and commercial, with various capabilities. I recommend you use the fantastic JuMP library for Julia, which exposes a domain-specific language for modelling, along with interfaces to nearly all major solver packages. (Even if you don’t know Julia, this is a great and easy way to start!) If you’d rather use Python, you can use Google’s OR-Tools or PuLP for linear programming.

        +

        There are many solvers available, both free and commercial, with various capabilities. I recommend you use the fantastic JuMP
        +
        +
        +
        +         library for Julia, which exposes a domain-specific language for modelling, along with interfaces to nearly all major solver packages. (Even if you don’t know Julia, this is a great and easy way to start!) If you’d rather use Python, you can use Google’s OR-Tools or PuLP for linear programming.

        Regarding solvers, there is a list of solvers on JuMP’s documentation, with their capabilities and their license. Free solvers include GLPK (linear programming), Ipopt (non-linear programming), and SCIP (mixed-integer linear programming).

        Commercial solvers often have better performance, and some of them propose a free academic license: MOSEK, Gurobi, and IBM CPLEX in particular all offer free academic licenses and work very well with JuMP.

        Another awesome resource is the NEOS Server. It offers free computing resources for numerical optimization, including all major free and commercial solvers! You can submit jobs on it in a standard format, or interface your favourite programming language with it. The fact that such an amazing resource exists for free, for everyone is extraordinary. They also have an accompanying book, the NEOS Guide, containing many case studies and description of problem types. The taxonomy may be particularly useful.

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a/_site/posts/operations-research-references.html +++ b/_site/posts/operations-research-references.html @@ -61,18 +61,30 @@

        Introduction and modelling

        For an overall introduction, I recommend Wentzel (1988). It is an old book, published by Mir Publications, a Soviet publisher which published many excellent scientific textbooks Mir also published Physics for Everyone by Lev Landau and Alexander Kitaigorodsky, a three-volume introduction to physics that is really accessible. Together with Feynman’s famous lectures, I read them (in French) when I was a kid, and it was the best introduction I could possibly have to the subject.

        -        . It is out of print, but it is available on Archive.org. The book is quite old, but everything presented is still extremely relevant today. It requires absolutely no background, and covers everything: a general introduction to the field, linear programming, dynamic programming, Markov processes and queues, Monte Carlo methods, and game theory. Even if you already know some of these topics, the presentations is so clear that it is a pleasure to read! (In particular, it is one of the best presentations of dynamic programming that I have ever read. The explanation of the simplex algorithm is also excellent.)

        +. It is out of print, but it is available on Archive.org
        +
        +
        +
        +        . The book is quite old, but everything presented is still extremely relevant today. It requires absolutely no background, and covers everything: a general introduction to the field, linear programming, dynamic programming, Markov processes and queues, Monte Carlo methods, and game theory. Even if you already know some of these topics, the presentations is so clear that it is a pleasure to read! (In particular, it is one of the best presentations of dynamic programming that I have ever read. The explanation of the simplex algorithm is also excellent.)

        If you are interested in optimization, the first thing you have to learn is modelling, i.e. transforming your problem (described in natural language, often from a particular industrial application) into a mathematical programme. The mathematical programme is the structure on which you will be able to apply an algorithm to find an optimal solution. Even if (like me) you are initially more interested in the algorithmic side of things, learning to create models will shed a lot of light on the overall process, and will give you more insight in general on the reasoning behind algorithms.

        -

        The best book I have read on the subject is Williams (2013). It contains a lot of concrete, step-by-step examples on concrete applications, in a multitude of domains, and remains very easy to read and to follow. It covers nearly every type of problem, so it is very useful as a reference. When you encounter a concrete problem in real life afterwards, you will know how to construct an appropriate model, and in the process you will often identify a common type of problem. The book then gives plenty of advice on how to approach each type of problem. Finally, it is also a great resource to build a “mental map” of the field, avoiding getting lost in the jungle of linear, stochastic, mixed integer, quadratic, and other network problems.

        +

        The best book I have read on the subject is Williams (2013)
        +
        +
        +
        +        . It contains a lot of concrete, step-by-step examples on concrete applications, in a multitude of domains, and remains very easy to read and to follow. It covers nearly every type of problem, so it is very useful as a reference. When you encounter a concrete problem in real life afterwards, you will know how to construct an appropriate model, and in the process you will often identify a common type of problem. The book then gives plenty of advice on how to approach each type of problem. Finally, it is also a great resource to build a “mental map” of the field, avoiding getting lost in the jungle of linear, stochastic, mixed integer, quadratic, and other network problems.

        Another interesting resource is the freely available MOSEK Modeling Cookbook, covering many types of problems, with more mathematical details than in Williams (2013). It is built for people wanting to use the commercial MOSEK solver, so it could be useful if you plan to use a solver package like this one (more details on solvers below).

        Theory and algorithms

        -

        The basic algorithm for optimization is the simplex algorithm, developed by Dantzig in the 1940s to solve linear programming problems. It is the one of the main building blocks for mathematical optimization, and is used and referenced extensively in all kinds of approaches. As such, it is really important to understand it in detail. There are many books on the subject, but I especially liked Chvátal (1983) (out of print, but you can find cheap used versions on Amazon). It covers everything there is to know on the simplex algorithms (step-by-step explanations with simple examples, correctness and complexity analysis, computational and implementation considerations) and to many applications. I think it is overall the best introduction. Vanderbei (2014) follows a very similar outline, but contains more recent computational considerationsFor all the details about practical implementations of the simplex algorithm, Maros (2003) is dedicated to the computational aspects and contains everything you will need.
        +

        The basic algorithm for optimization is the simplex algorithm, developed by Dantzig in the 1940s to solve linear programming problems. It is the one of the main building blocks for mathematical optimization, and is used and referenced extensively in all kinds of approaches. As such, it is really important to understand it in detail. There are many books on the subject, but I especially liked Chvátal (1983) (out of print, but you can find cheap used versions on Amazon). It covers everything there is to know on the simplex algorithms (step-by-step explanations with simple examples, correctness and complexity analysis, computational and implementation considerations) and to many applications. I think it is overall the best introduction. Vanderbei (2014) follows a very similar outline, but contains more recent computational considerationsFor all the details about practical implementations of the simplex algorithm, Maros (2003) is dedicated to the computational aspects and contains everything you will need.

        . (The author also has lecture slides.)

        For more books on linear programming, the two books Dantzig (1997), Dantzig (2003) are very complete, if somewhat more mathematically advanced. Bertsimas and Tsitsiklis (1997) is also a great reference, if you can find it.

        -

        For all the other subfields, this great StackExchange answer contains a lot of useful references, including most of the above. Of particular note are Peyré and Cuturi (2019) for optimal transport, Boyd (2004) for convex optimization (freely available online), and Nocedal (2006) for numerical optimization. Kochenderfer (2019) is not in the list (because it is very recent) but is also excellent, with examples in Julia covering nearly every kind of optimization algorithms.

        +

        For all the other subfields, this great StackExchange answer contains a lot of useful references, including most of the above. Of particular note are Peyré and Cuturi (2019) for optimal transport, Boyd (2004) for convex optimization (freely available online), and Nocedal (2006) for numerical optimization. Kochenderfer (2019)
        +
        +
        +
        +         is not in the list (because it is very recent) but is also excellent, with examples in Julia covering nearly every kind of optimization algorithms.

        Online courses

        -

        If you would like to watch video lectures, there are a few good opportunities freely available online, in particular on MIT OpenCourseWare. The list of courses at MIT is available on their webpage. I haven’t actually looked in details at the courses contentI am more comfortable reading books than watching lecture videos online. Although I liked attending classes during my studies, I do not have the same feeling in front of a video. When I read, I can re-read three times the same sentence, pause to look up something, or skim a few paragraphs. I find that the inability to do that with a video diminishes greatly my ability to concentrate.
        +

        If you would like to watch video lectures, there are a few good opportunities freely available online, in particular on MIT OpenCourseWare. The list of courses at MIT is available on their webpage. I haven’t actually looked in details at the courses contentI am more comfortable reading books than watching lecture videos online. Although I liked attending classes during my studies, I do not have the same feeling in front of a video. When I read, I can re-read three times the same sentence, pause to look up something, or skim a few paragraphs. I find that the inability to do that with a video diminishes greatly my ability to concentrate.

        , so I cannot vouch for them directly, but MIT courses are generally of excellent quality. Most courses are also taught by Bertsimas and Bertsekas, who are very famous and wrote many excellent books.

        Of particular notes are:

        @@ -83,12 +95,16 @@
      • Algebraic Techniques and Semidefinite Optimization,
      • Integer Programming and Combinatorial Optimization.
      -

      Another interesting course I found online is Deep Learning in Discrete Optimization, at Johns Hopkins It is taught by William Cook, who is the author of In Pursuit of the Traveling Salesman, a nice introduction to the TSP problem in a readable form.
      +

      Another interesting course I found online is Deep Learning in Discrete Optimization, at Johns Hopkins It is taught by William Cook, who is the author of In Pursuit of the Traveling Salesman, a nice introduction to the TSP problem in a readable form.

      . It contains an interesting overview of deep learning and integer programming, with a focus on connections, and applications to recent research areas in ML (reinforcement learning, attention, etc.).

      Solvers and computational resources

      When you start reading about modelling and algorithms, I recommend you try solving a few problems yourself, either by hand for small instances, or using an existing solver. It will allow you to follow the examples in books, while also practising your modelling skills. You will also get an intuition of what is difficult to model and to solve.

      -

      There are many solvers available, both free and commercial, with various capabilities. I recommend you use the fantastic JuMP library for Julia, which exposes a domain-specific language for modelling, along with interfaces to nearly all major solver packages. (Even if you don’t know Julia, this is a great and easy way to start!) If you’d rather use Python, you can use Google’s OR-Tools or PuLP for linear programming.

      +

      There are many solvers available, both free and commercial, with various capabilities. I recommend you use the fantastic JuMP
      +
      +
      +
      +       library for Julia, which exposes a domain-specific language for modelling, along with interfaces to nearly all major solver packages. (Even if you don’t know Julia, this is a great and easy way to start!) If you’d rather use Python, you can use Google’s OR-Tools or PuLP for linear programming.

      Regarding solvers, there is a list of solvers on JuMP’s documentation, with their capabilities and their license. Free solvers include GLPK (linear programming), Ipopt (non-linear programming), and SCIP (mixed-integer linear programming).

      Commercial solvers often have better performance, and some of them propose a free academic license: MOSEK, Gurobi, and IBM CPLEX in particular all offer free academic licenses and work very well with JuMP.

      Another awesome resource is the NEOS Server. It offers free computing resources for numerical optimization, including all major free and commercial solvers! You can submit jobs on it in a standard format, or interface your favourite programming language with it. The fact that such an amazing resource exists for free, for everyone is extraordinary. They also have an accompanying book, the NEOS Guide, containing many case studies and description of problem types. The taxonomy may be particularly useful.

      diff --git a/_site/rss.xml b/_site/rss.xml index a90e537..73dbb87 100644 --- a/_site/rss.xml +++ b/_site/rss.xml @@ -28,18 +28,30 @@

      Introduction and modelling

      For an overall introduction, I recommend Wentzel (1988). It is an old book, published by Mir Publications, a Soviet publisher which published many excellent scientific textbooks Mir also published Physics for Everyone by Lev Landau and Alexander Kitaigorodsky, a three-volume introduction to physics that is really accessible. Together with Feynman’s famous lectures, I read them (in French) when I was a kid, and it was the best introduction I could possibly have to the subject.

      -      . It is out of print, but it is available on Archive.org. The book is quite old, but everything presented is still extremely relevant today. It requires absolutely no background, and covers everything: a general introduction to the field, linear programming, dynamic programming, Markov processes and queues, Monte Carlo methods, and game theory. Even if you already know some of these topics, the presentations is so clear that it is a pleasure to read! (In particular, it is one of the best presentations of dynamic programming that I have ever read. The explanation of the simplex algorithm is also excellent.)

      +. It is out of print, but it is available on Archive.org
      +
      +
      +
      +      . The book is quite old, but everything presented is still extremely relevant today. It requires absolutely no background, and covers everything: a general introduction to the field, linear programming, dynamic programming, Markov processes and queues, Monte Carlo methods, and game theory. Even if you already know some of these topics, the presentations is so clear that it is a pleasure to read! (In particular, it is one of the best presentations of dynamic programming that I have ever read. The explanation of the simplex algorithm is also excellent.)

      If you are interested in optimization, the first thing you have to learn is modelling, i.e. transforming your problem (described in natural language, often from a particular industrial application) into a mathematical programme. The mathematical programme is the structure on which you will be able to apply an algorithm to find an optimal solution. Even if (like me) you are initially more interested in the algorithmic side of things, learning to create models will shed a lot of light on the overall process, and will give you more insight in general on the reasoning behind algorithms.

      -

      The best book I have read on the subject is Williams (2013). It contains a lot of concrete, step-by-step examples on concrete applications, in a multitude of domains, and remains very easy to read and to follow. It covers nearly every type of problem, so it is very useful as a reference. When you encounter a concrete problem in real life afterwards, you will know how to construct an appropriate model, and in the process you will often identify a common type of problem. The book then gives plenty of advice on how to approach each type of problem. Finally, it is also a great resource to build a “mental map” of the field, avoiding getting lost in the jungle of linear, stochastic, mixed integer, quadratic, and other network problems.

      +

      The best book I have read on the subject is Williams (2013)
      +
      +
      +
      +      . It contains a lot of concrete, step-by-step examples on concrete applications, in a multitude of domains, and remains very easy to read and to follow. It covers nearly every type of problem, so it is very useful as a reference. When you encounter a concrete problem in real life afterwards, you will know how to construct an appropriate model, and in the process you will often identify a common type of problem. The book then gives plenty of advice on how to approach each type of problem. Finally, it is also a great resource to build a “mental map” of the field, avoiding getting lost in the jungle of linear, stochastic, mixed integer, quadratic, and other network problems.

      Another interesting resource is the freely available MOSEK Modeling Cookbook, covering many types of problems, with more mathematical details than in Williams (2013). It is built for people wanting to use the commercial MOSEK solver, so it could be useful if you plan to use a solver package like this one (more details on solvers below).

      Theory and algorithms

      -

      The basic algorithm for optimization is the simplex algorithm, developed by Dantzig in the 1940s to solve linear programming problems. It is the one of the main building blocks for mathematical optimization, and is used and referenced extensively in all kinds of approaches. As such, it is really important to understand it in detail. There are many books on the subject, but I especially liked Chvátal (1983) (out of print, but you can find cheap used versions on Amazon). It covers everything there is to know on the simplex algorithms (step-by-step explanations with simple examples, correctness and complexity analysis, computational and implementation considerations) and to many applications. I think it is overall the best introduction. Vanderbei (2014) follows a very similar outline, but contains more recent computational considerationsFor all the details about practical implementations of the simplex algorithm, Maros (2003) is dedicated to the computational aspects and contains everything you will need.
      +

      The basic algorithm for optimization is the simplex algorithm, developed by Dantzig in the 1940s to solve linear programming problems. It is the one of the main building blocks for mathematical optimization, and is used and referenced extensively in all kinds of approaches. As such, it is really important to understand it in detail. There are many books on the subject, but I especially liked Chvátal (1983) (out of print, but you can find cheap used versions on Amazon). It covers everything there is to know on the simplex algorithms (step-by-step explanations with simple examples, correctness and complexity analysis, computational and implementation considerations) and to many applications. I think it is overall the best introduction. Vanderbei (2014) follows a very similar outline, but contains more recent computational considerationsFor all the details about practical implementations of the simplex algorithm, Maros (2003) is dedicated to the computational aspects and contains everything you will need.

      . (The author also has lecture slides.)

      For more books on linear programming, the two books Dantzig (1997), Dantzig (2003) are very complete, if somewhat more mathematically advanced. Bertsimas and Tsitsiklis (1997) is also a great reference, if you can find it.

      -

      For all the other subfields, this great StackExchange answer contains a lot of useful references, including most of the above. Of particular note are Peyré and Cuturi (2019) for optimal transport, Boyd (2004) for convex optimization (freely available online), and Nocedal (2006) for numerical optimization. Kochenderfer (2019) is not in the list (because it is very recent) but is also excellent, with examples in Julia covering nearly every kind of optimization algorithms.

      +

      For all the other subfields, this great StackExchange answer contains a lot of useful references, including most of the above. Of particular note are Peyré and Cuturi (2019) for optimal transport, Boyd (2004) for convex optimization (freely available online), and Nocedal (2006) for numerical optimization. Kochenderfer (2019)
      +
      +
      +
      +       is not in the list (because it is very recent) but is also excellent, with examples in Julia covering nearly every kind of optimization algorithms.

      Online courses

      -

      If you would like to watch video lectures, there are a few good opportunities freely available online, in particular on MIT OpenCourseWare. The list of courses at MIT is available on their webpage. I haven’t actually looked in details at the courses contentI am more comfortable reading books than watching lecture videos online. Although I liked attending classes during my studies, I do not have the same feeling in front of a video. When I read, I can re-read three times the same sentence, pause to look up something, or skim a few paragraphs. I find that the inability to do that with a video diminishes greatly my ability to concentrate.
      +

      If you would like to watch video lectures, there are a few good opportunities freely available online, in particular on MIT OpenCourseWare. The list of courses at MIT is available on their webpage. I haven’t actually looked in details at the courses contentI am more comfortable reading books than watching lecture videos online. Although I liked attending classes during my studies, I do not have the same feeling in front of a video. When I read, I can re-read three times the same sentence, pause to look up something, or skim a few paragraphs. I find that the inability to do that with a video diminishes greatly my ability to concentrate.

      , so I cannot vouch for them directly, but MIT courses are generally of excellent quality. Most courses are also taught by Bertsimas and Bertsekas, who are very famous and wrote many excellent books.

      Of particular notes are:

      @@ -50,12 +62,16 @@
    • Algebraic Techniques and Semidefinite Optimization,
    • Integer Programming and Combinatorial Optimization.
    -

    Another interesting course I found online is Deep Learning in Discrete Optimization, at Johns Hopkins It is taught by William Cook, who is the author of In Pursuit of the Traveling Salesman, a nice introduction to the TSP problem in a readable form.
    +

    Another interesting course I found online is Deep Learning in Discrete Optimization, at Johns Hopkins It is taught by William Cook, who is the author of In Pursuit of the Traveling Salesman, a nice introduction to the TSP problem in a readable form.

    . It contains an interesting overview of deep learning and integer programming, with a focus on connections, and applications to recent research areas in ML (reinforcement learning, attention, etc.).

    Solvers and computational resources

    When you start reading about modelling and algorithms, I recommend you try solving a few problems yourself, either by hand for small instances, or using an existing solver. It will allow you to follow the examples in books, while also practising your modelling skills. You will also get an intuition of what is difficult to model and to solve.

    -

    There are many solvers available, both free and commercial, with various capabilities. I recommend you use the fantastic JuMP library for Julia, which exposes a domain-specific language for modelling, along with interfaces to nearly all major solver packages. (Even if you don’t know Julia, this is a great and easy way to start!) If you’d rather use Python, you can use Google’s OR-Tools or PuLP for linear programming.

    +

    There are many solvers available, both free and commercial, with various capabilities. I recommend you use the fantastic JuMP
    +
    +
    +
    +     library for Julia, which exposes a domain-specific language for modelling, along with interfaces to nearly all major solver packages. (Even if you don’t know Julia, this is a great and easy way to start!) If you’d rather use Python, you can use Google’s OR-Tools or PuLP for linear programming.

    Regarding solvers, there is a list of solvers on JuMP’s documentation, with their capabilities and their license. Free solvers include GLPK (linear programming), Ipopt (non-linear programming), and SCIP (mixed-integer linear programming).

    Commercial solvers often have better performance, and some of them propose a free academic license: MOSEK, Gurobi, and IBM CPLEX in particular all offer free academic licenses and work very well with JuMP.

    Another awesome resource is the NEOS Server. It offers free computing resources for numerical optimization, including all major free and commercial solvers! You can submit jobs on it in a standard format, or interface your favourite programming language with it. The fact that such an amazing resource exists for free, for everyone is extraordinary. They also have an accompanying book, the NEOS Guide, containing many case studies and description of problem types. The taxonomy may be particularly useful.

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zwbn0+iIc=GaZ)*m5`9*WDlavx8P=PH#~bBM3U^%p*GTSYh)uEmRToCejfhz1IqoY7 z_gM;e?wzoJd+Isi%Q0O|GU9xeov#z4zSs)kW44uAmg0Jt_5bM7Fo@F0d_}Iw)0;gn za}$a2p&-I!r^7y$3z^SZae!CACoEnZa<-Leh59xi5!nJi9 zA0Fb`AVvDlBv9j{f^RBsC5kUxG`frk|G1uX61yXz8xm+(LP^GDCoK^_*+T6&fD=auUuT{{(bgXT!8^SV-TE5_(b#?YGB)(sx1X0$Rf7Hqsz{>*5T)duT3x1Oo w67Zz^+YQ;J+tqR;X=UNLbpNt-@g@zDeUhvURfgoWi!z_=?i#MmkD2-NAK#zlcK`qY literal 0 HcmV?d00001 diff --git a/posts/operations-research-references.org b/posts/operations-research-references.org index 3bcb33b..b6201c4 100644 --- a/posts/operations-research-references.org +++ b/posts/operations-research-references.org @@ -53,17 +53,21 @@ programming, stochastic processes, etc. For an overall introduction, I recommend cite:wentzel1988_operat. It is an old book, published by Mir Publications, a Soviet publisher which published many excellent scientific textbooks[fn:mir]. It is out -of print, but it is available [[https://archive.org/details/WentzelOperationsResearchMir1983][on Archive.org]]. The book is quite old, -but everything presented is still extremely relevant today. It -requires absolutely no background, and covers everything: a general -introduction to the field, linear programming, dynamic programming, -Markov processes and queues, Monte Carlo methods, and game -theory. Even if you already know some of these topics, the +of print, but it is available [[https://archive.org/details/WentzelOperationsResearchMir1983][on Archive.org]][fn:wentzel]. The book is +quite old, but everything presented is still extremely relevant +today. It requires absolutely no background, and covers everything: a +general introduction to the field, linear programming, dynamic +programming, Markov processes and queues, Monte Carlo methods, and +game theory. Even if you already know some of these topics, the presentations is so clear that it is a pleasure to read! (In particular, it is one of the best presentations of dynamic programming that I have ever read. The explanation of the simplex algorithm is also excellent.) +[fn:wentzel] {-} +#+ATTR_HTML: :width 200px +[[file:/images/or_references/wentzel.jpg]] + [fn:mir] {-} Mir also published [[https://mirtitles.org/2011/06/03/physics-for-everyone/][/Physics for Everyone/]] by Lev Landau and Alexander Kitaigorodsky, a three-volume introduction to physics that is really accessible. Together with Feynman's famous [[https://www.feynmanlectures.caltech.edu/][lectures]], I @@ -82,18 +86,23 @@ of light on the overall process, and will give you more insight in general on the reasoning behind algorithms. The best book I have read on the subject is -cite:williams2013_model. It contains a lot of concrete, step-by-step -examples on concrete applications, in a multitude of domains, and -remains very easy to read and to follow. It covers nearly every type -of problem, so it is very useful as a reference. When you encounter a -concrete problem in real life afterwards, you will know how to -construct an appropriate model, and in the process you will often -identify a common type of problem. The book then gives plenty of +cite:williams2013_model[fn:williams]. It contains a lot of concrete, +step-by-step examples on concrete applications, in a multitude of +domains, and remains very easy to read and to follow. It covers nearly +every type of problem, so it is very useful as a reference. When you +encounter a concrete problem in real life afterwards, you will know +how to construct an appropriate model, and in the process you will +often identify a common type of problem. The book then gives plenty of advice on how to approach each type of problem. Finally, it is also a great resource to build a "mental map" of the field, avoiding getting lost in the jungle of linear, stochastic, mixed integer, quadratic, and other network problems. +[fn:williams] {-} +#+ATTR_HTML: :width 200px +[[file:/images/or_references/williams.jpg]] + + Another interesting resource is the freely available [[https://docs.mosek.com/modeling-cookbook/index.html][MOSEK Modeling Cookbook]], covering many types of problems, with more mathematical details than in cite:williams2013_model. It is built for people @@ -135,9 +144,15 @@ a lot of useful references, including most of the above. Of particular note are cite:peyreComputationalOptimalTransport2019 for optimal transport, cite:boyd2004_convex for convex optimization ([[https://web.stanford.edu/~boyd/cvxbook/][freely available online]]), and cite:nocedal2006_numer for numerical -optimization. cite:kochenderfer2019_algor is not in the list (because -it is very recent) but is also excellent, with examples in Julia -covering nearly every kind of optimization algorithms. +optimization. cite:kochenderfer2019_algor[fn:kochenderfer] is not in +the list (because it is very recent) but is also excellent, with +examples in Julia covering nearly every kind of optimization +algorithms. + +[fn:kochenderfer] {-} +#+ATTR_HTML: :width 200px +[[file:/images/or_references/kochenderfer.jpg]] + ** Online courses @@ -186,12 +201,17 @@ skills. You will also get an intuition of what is difficult to model and to solve. There are many solvers available, both free and commercial, with -various capabilities. I recommend you use the fantastic [[https://github.com/JuliaOpt/JuMP.jl][JuMP]] library -for Julia, which exposes a domain-specific language for modelling, -along with interfaces to nearly all major solver packages. (Even if -you don't know Julia, this is a great and easy way to start!) If you'd -rather use Python, you can use Google's [[https://developers.google.com/optimization/introduction/python][OR-Tools]] or [[https://github.com/coin-or/pulp][PuLP]] for linear -programming. +various capabilities. I recommend you use the fantastic [[https://github.com/JuliaOpt/JuMP.jl][JuMP]][fn:jump] +library for Julia, which exposes a domain-specific language for +modelling, along with interfaces to nearly all major solver +packages. (Even if you don't know Julia, this is a great and easy way +to start!) If you'd rather use Python, you can use Google's [[https://developers.google.com/optimization/introduction/python][OR-Tools]] +or [[https://github.com/coin-or/pulp][PuLP]] for linear programming. + +[fn:jump] {-} +#+ATTR_HTML: :width 250px +[[file:/images/or_references/jump.svg]] + Regarding solvers, there is a [[http://www.juliaopt.org/JuMP.jl/stable/installation/#Getting-Solvers-1][list of solvers]] on JuMP's documentation, with their capabilities and their license. Free solvers include [[https://www.gnu.org/software/glpk/][GLPK]]