A sequential optimality condition for Mathematical Programs with equilibrium constraints based on a nonsmooth formulation

Abstract

Abstract Explicitly nonsmooth reformulations of mathematical programs with equilibrium constraints (MPEC) described by smooth functions are investigated. A sequential optimality condition ($\epsilon $-ANOC) previously developed for nonsmooth optimization problems is adapted to suit the reformulations under analysis. Relationships between $\epsilon $-ANOC and sequential optimality conditions especially crafted for MPEC are established. It is revealed that approaches developed for nonsmooth optimization improve the understanding of smooth problems with ill-conditioned geometries, which is the case for MPEC. Moreover, based on the availability of algorithms capable of generating $\epsilon $-ANOC sequences, illustrative experiments are reported in which difficult problems are successfully solved.