Improved Convergence Properties of the Relaxation Schemes of Kadrani et al. and Kanzow and Schwartz for MPEC

This paper concentrates on improving the convergence properties of the relaxation schemes introduced by Kadrani et al. and Kanzow and Schwartz for mathematical program with equilibrium constraints (MPEC) by weakening the original constraint qualifications. It has been known that MPEC relaxed constant positive-linear dependence (MPEC-RCPLD) is a class of extremely weak constraint qualifications for MPEC, which can be strictly implied by MPEC relaxed constant rank constraint qualification (MPEC-RCRCQ) and MPEC relaxed constant positive-linear dependence (MPEC-rCPLD), of course also by the MPEC constant positive-linear dependence (MPEC-CPLD). We show that any accumulation point of stationary points of these two approximation problems is M-stationarity under the MPEC-RCPLD constraint qualification, and further show that the accumulation point can even be S-stationarity coupled with the asymptotically weak nondegeneracy condition.