A New Regularization Scheme for Mathematical Programs with Complementarity Constraints

Abstract

We propose a new regularization scheme for mathematical programs with complementarity constraints (MPCC) by relaxing all the constraints of the complementarity system. We show that, under the MPCC-linear independence constraint qualifications (MPCC-LICQ), the Lagrange multipliers exist for this regularization. Our method has strong convergence properties under MPCC-linear independence constraint qualifications and some weak conditions of the strict complementarity. In particular, under MPCC-LICQ, it is shown that any accumulation point of the regularized stationary points is M-stationary for the MPCC problem, and if the asymptotically weak nondegeneracy condition holds at a stationary point of the regularized problem, then it is strongly stationary. An algorithm for solving the proposed regularization is presented and numerical experiments are reported. Some comparisons with other methods are discussed with illustrative examples.