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Add references for other optimization problems

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Dimitri Lozeve 2020-05-26 18:06:23 +02:00
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@ -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 <<solvers>>