On quasidifferentiable mathematical programs with equilibrium constraints

Abstract The aim of this article is to study mathematical programs with equilibrium constraints involving quasidifferentiable functions, denoted by QMPEC, and to synthesize suitable optimality conditions. We first derive Fritz-John (FJ) necessary optimality conditions with Lagrange multipliers depending upon the choice of superdifferentials. We introduce a suitable variant of no nonzero abnormal multiplier constraint qualification for the QMPEC, denoted by NNAMCQ-QMPEC, and derive Karush-Kuhn-Tucker (KKT) necessary optimality conditions. We also propose some conditions under which the Lagrange multipliers do not depend upon the choice of superdifferentials. Further, we prove several sufficient optimality conditions for a weak stationary point to be optimal for the QMPEC under suitable choice of generalized convex functions.