A class of smoothing methods for mathematical programs with complementarity constraints

Mathematical programs with complementarity constraints (MPCC) is an important subclass of MPEC, and for conventional MPEC, we can transform it into the MPCC form in some manner. It is a nature way to solve MPCC by constructing a suitable approximation of the primal problem. In this paper, we present a class of smoothing methods for MPCC, it is a broader approximation, and by selecting an available probability density function, we can obtain a corresponding approximation of MPCC. We show that the linear independence constraint qualification holds for the class of smooth methods under some conditions. We also analyze the convergence properties of the accumulated point gotten by the class of smooth methods.