Background
Type: Article

Optimality Conditions for Nonsmooth Equilibrium Problems via Hadamard Directional Derivative

Journal: Set-Valued and Variational Analysis (18770541)Year: 1 September 2016Volume: 24Issue: Pages: 483 - 497
DOI:10.1007/s11228-015-0354-3Language: English

Abstract

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. © 2015, Springer Science+Business Media Dordrecht.