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Convergence properties of a first order regularized-penalized method for MPCC

This paper aims at developing a new effective approach for solving mathematical programs with complementarity constraints (MPCCs). These mathematical programs are difficult optimization problems that do not satisfy the majority of the usual constraint qualifications at any feasible point for standard nonlinear optimization, and there are various stationarity concepts that are specially defined for MPCCs. In this paper, we suggest a relaxation-penalty approach that combines between the regularization scheme for MPCCs and the penalty method. We establish the convergence analysis of this approach and we further give some sufficient conditions to ensure that cluster points of the first order regularized-penalized points are feasible and Strong stationary (S-stationary) points for MPCCs.