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I’ve studied convex optimization already with Boyd & Vandenberghe's book. Now I need to learn non-convex optimization. What are the best/most common texts for this? Need to learn a general overview for a company project. Have undergrad level of convex optimization. Have taken general 2nd/3rd year linear algebra class. Have taken calculus series, probability/stochastic processes, and linear algebra series. Have not taken analysis. Haven’t considered any books yet. I tried searching this up prior to my question, but I really couldn’t find much.

Edit: studied from Boyd. Covered 75% of Practical Mathematical Optimization contents, but all of the main concepts covered. Looking for a general intro text including just a general overview of the field. Preferably global optimization.

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  • $\begingroup$ Yes. Taken calculus series, and linear algebra series, and convex optimization, and probability/stochastic processes. $\endgroup$ Commented Jul 10, 2022 at 16:10
  • $\begingroup$ Have you covered all (or nearly all) of the topics from, say, Practical Mathematical Optimization by Snyman & Wilke? $\endgroup$
    – J W
    Commented Jul 10, 2022 at 18:23
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    $\begingroup$ Are you interested in finding local minima of smooth nonconvex optimization problems? This is what was traditionally studied as "nonlinear programming" and there are many textbooks. Or, are you interested in finding a global minimum of a smooth nonconvex optimization problem? This is "global optimization" $\endgroup$ Commented Jul 14, 2022 at 0:31
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    $\begingroup$ Edited. Added more info $\endgroup$ Commented Jul 15, 2022 at 15:14
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    $\begingroup$ This question is about references for studying mathematics rather than for teaching mathematics. It seems to me more appropriate for the main mathematics stackoverflow. $\endgroup$
    – Dan Fox
    Commented Jul 29, 2022 at 10:34

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Approaches to global optimization problems are broadly divided into deterministic methods (with some convergence guarantee, but requiring some assumptions on the objective function and constraints) such as branch-and-bound and stochastic (or heuristic) methods such as simulated annealing and tabu search that may work well in practice but do not guarantee convergence to a globally optimal solution.

Some references for deterministic methods:

Floudas, Christodoulos A. Deterministic global optimization: theory, methods and applications. Vol. 37. Springer Science & Business Media, 2013.

Horst, Reiner, and Hoang Tuy. Global optimization: Deterministic approaches. Springer Science & Business Media, 2013.

A reference for stochastic/heuristic methods:

Horst, Reiner, and Panos M. Pardalos, eds. Handbook of global optimization. Vol. 2. Springer Science & Business Media, 2013. (Volume 1 covers deterministic methods.)

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