How to Compute a M-stationary point 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, \cite{kanzow2015}, that relaxation methods with approximate stationary points fail to give guarantee of convergence. We show that by defining 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.

Year : 2017