A generalized project metric algorithm for mathematical programs with equilibrium constraints

This paper discusses a kind of mathematical programs with equilibrium constraints (MPEC for short). By using a complementarity function and a kind of disturbed technique, the original (MPEC) problem is transformed into a nonlinear equality and inequality constrained optimization problem. Then, we combine a generalized gradient projection matrix with penalty function technique to given a generalized project metric algorithm with arbitrary initial point for the (MPEC) problems. In order to avoid Mataros effect, a high-order revised direction is obtained by an explicit formula. Under some relative weaker conditions, the proposed method is proved to possess global convergence and superlinear convergence.