INVITED PAPER A TUTORIAL NOTE ON A CONVEXIFICATION PROCEDURE IN NON-CONVEX SEMI-INFINITE OPTIMIZATION

Abstract

In this tutorial note we consider the class of non-convex semi-infinite optimization problems which are defined by (one or) finitely many objective functions as well as infinitely many constraints in a finite- dimensional space. We present an overview of recent results on the so-called p-power transformation which changes the original problem equivalently locally around a solution point. This transformation
is a convexification procedure for the Lagrangian where the functions in the original problem are substituted by their p-th powers. As a consequence, the convexity of the so-transformed Lagrangian allows the application of local duality theory and corresponding solution methods locally around this solution point of the original problem