A sequential smooth penalization approach to mathematical programs with complementarity constraints

In this paper, a mathematical program with complementarity constraints (MPCC) is reformulated as a nonsmooth constrained mathematical program via the Fischer-Burmeister function. Smooth penalty functions are used to treat this nonsmooth constrained program. Under linear independence constraint qualification, and upper level strict complementarity condition, together with some other mild conditions, we prove that the limit point of stationary points satisfying second-order necessary conditions of unconstrained penalized problems is a strongly stationary point, hence a B-stationary point of the original MPCC. Furthermore, this limit point also satisfies a second-order necessary condition of the original MPCC. Numerical results are presented to test the performance of this method.