Optimality conditions for MPECs in terms of directional upper convexifactors

Abstract

In this paper, we investigate necessary and sufficient optimality conditions for mathematical programs with equilibrium constraints. For this goal, we introduce an appropriate type of MPEC regularity condition and a stationary concept given in terms of directional upper convexificators and directional upper semi-regular convexificators. The appearing functions are not necessarily smooth/locally Lipschitz/convex/continuous, and the continuity directions’ sets are not assumed to be compact or convex. Finally, notions of directional pseudoconvexity and directional quasiconvexity are used to establish sufficient optimality conditions for MPECs.