In this paper, we consider a mathematical program with equilibrium constraints
(MPEC) formulated as a mathematical program with complementarity constraints. We
obtain necessary conditions of Fritz John (FJ) and Karush-Kuhn-Tucker (KKT) types for
a nonsmooth (MPEC) problem in terms of the lower Hadamard directional derivative. In
particular sufficient conditions for MPECs are given where the involved functions have
pseudoconvex sublevel sets. The functions with pseudoconvex sublevel sets is a class of
generalized convex functions that include quasiconvex functions.
