Nondifferentiable multiplier rules for optimization problems with equilibrium constraints

Abstract

We consider a mathematical program with equilibrium constraints (MPBC). First we obtain a Lagrange multiplier rule based on the linear sub differential involving equality, inequality and set constraints. Then we propose new constraint qualifications for M-stationary condition to hold. Finally we establish the Fritz John and Karush-Kuhn Tucker M-stationary necessary conditions for a nonsmooth (MPBC) based on the Michel-Penot subdifferential. © Heldermann Verlag.