Does convexity arise in optimization naturally?

Abstract

Convexity is one of the conditions that any researcher may desire to have when dealing with problems in Optimization. Thus, the lack of standard convexity provides an interesting challenge in mathematics. In this talk we show various instances from mathematical programming, differential inclusions to calculus of variations, where convexity is present in one way or in another. Among the issues to be described lie: strong duality, KKT optimality conditions; joint-range and the S-lemma for a pair of (not necessarily homogeneous) quadratic functions; optimal value functions; local optimality implies global; weak convergence implies strong.

This research is supported in part by CONICYT-Chile through FONDE- CYT 115-0973 and by Center for Mathematical Modeling (CMM), Universidad de Chile.

Posted on Nov 3, 2016 in Optimization and Equilibrium, Seminars