Superlinear Convergence of a Smooth Approximation Method for Mathematical Programs with Nonlinear Complementarity Constraints

Abstract

Mathematical programs with complementarity constraints (MPCC) is an important subclass of MPEC. It is a natural way to solve MPCC by constructing a suitable approximation of the primal problem. In this paper, we propose a new smoothing method for MPCC by using the aggregation technique. A new SQP algorithm for solving the MPCC problem is presented. At each iteration, the master direction is computed by solving a quadratic program, and the revised direction for avoiding the Maratos effect is generated by an explicit formula. As the non-degeneracy condition holds and the smoothing parameter tends to zero, the proposed SQP algorithm converges globally to an S-stationary point of the MPEC problem, its convergence rate is superlinear. Some preliminary numerical results are reported.