Nondifferentiable Multiplier Rules for Optimization Problems with Equilibrium Constraints

We consider a mathematical program with equilibrium constraints (MPEC). First we obtain a Lagrange multiplier rule based on the linear subdifferential 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 (MPEC) based on the Michel-Penot subdifferential.