Global Optimization and the Geometric Complementarity Problem

Abstract

We survey briefly recent studies on the relationship between global optimization and the problem of finding a point in the difference of two convex sets (Geometric Complementarity Problem GCP). This relationship is of interest because, for large problem classes, transcending stationarity is equivalent to a special GCP. Moreover, the complementarity viewpoint often leads to dimension reduction techniques which can substantially reduce the computational effort of solving certain special-structured global optimization problems.