How to Compute a Local Minimum of the MPCC

We discuss here the convergence of relaxation methods for MPCC with approximate sequence of stationary points by presenting a general framework to study these methods. It has been pointed out in the literature, [25], that relaxation methods with approximate stationary points fail to give guarantee of convergence. We show that by de ning a new strong approximate stationarity we can attain the desired goal of computing an M-stationary point. We also provide an algorithmic strategy to compute such point. Existence of strong approximate stationary point in the neighborhood of an M-stationary point is proved.