A second order inexact log-exponential regularization method for mathematical programs with complementarity constraints

In recent years, many methods have been presented to overcome the dif1 culties in solving mathe-matical programs with complementarity constraints (MPCC). The regularization methods are one prominent class of solution methods. This paper concerns the convergence properties and practical implementation of a log-exponential regularization method. We prove that, under MPCC-LICQ assumption, a limit point of a sequence generated by the log-exponential regularization method is an M-stationary point, if approxi-mate second order stationary conditions are satisfied. A second order primal-dual stabilized SQP method is presented to solve the regularized problems. The proposed method can generate the approximate second order stationary points of the regularized problems. Numerical results, demonstrating the effectiveness of our approach, are also presented.