An Inexact Solution Approach for the Mathematical Program with Complementarity Constraints

We propose an approach based on a penalty formulation and a relaxation scheme for mathematical programs with complementarity constraints (MPCC). We discuss the convergence analysis with a new strong approximate stationarity concept. The convergence of the sequence of strong approximate stationary points, generated by solving a family of regularized-penalized sub-problems, is investigated. Under the MPCC-Mangasarian-Fromovitz constraint qualifications (MPCC-MFCQ), we show that any accumulation point of the sequence of strong approximate stationary points of regularized-penalized sub-problems is a M-stationary point of the original MPCC.