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I am studying now convex sets and very interested in applications of them in Computer Science (maybe ACM problems) and other real life problems. Coud you please give some examples?

P.S. I am interested in examples that are strictly related to convex sets. And without this notion they would not be solved.

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  • $\begingroup$ A local minimum is a global minimum in the case of a convex set. This is very useful for optimization problems. In the case of strictly convex sets, the minimum is moreover unique. $\endgroup$
    – Peter
    Nov 16, 2016 at 13:39
  • $\begingroup$ Linear programming and least squares problems alone give a wide variety of applied convex optimization problems $\endgroup$
    – Ben Grossmann
    Nov 16, 2016 at 13:41
  • $\begingroup$ @Omnomnomnom, but I am interested in examples that are strictly related to convex sets. And without this notion they would not be solved. $\endgroup$
    – Turkhan Badalov
    Nov 16, 2016 at 13:43
  • $\begingroup$ What do you mean by "strictly related to convex sets"? Isn't any convex optimization problem "related" (whatever that means) to certain convex sets (such as the constraint set, and the epigraph of the objective function)? $\endgroup$
    – littleO
    Nov 16, 2016 at 13:47
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    $\begingroup$ The book Convex Optimization by Boyd and Vandenberghe (free online) is filled with applications which do not appear to be convex at first sight, and yet with clever tricks or techniques can be formulated as convex problems. $\endgroup$
    – littleO
    Nov 16, 2016 at 13:58

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Peter comment answer pretty well this question. It can be found misplaced at What are the main uses of Convex Functions? by Evgeny adding uniqueness. So, in my oppinion optimization is the key:

Every local extremum is also a global extremum and there exists only one such extremum.

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    $\begingroup$ Quasiconvex functions and unimodal functions offer the same advantage. Also, you seem to talk about functions rather than sets. They are related via the epigraph, but you talk about the optimum of a function. $\endgroup$
    – LinAlg
    Jan 30, 2017 at 15:14
  • $\begingroup$ Yes you are right. Anyway I can't offer any answer outside basic optimization theory. It's not my field of expertice. I'm whaiting for someone else answer this question. $\endgroup$
    – Ernesto Iglesias
    Jan 30, 2017 at 20:31

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