报告题目：A Relaxation Approximation Method for Regularized Mathematical Programs with Equilibrium Constraints

主 讲 人：郭磊   副教授

报告时间：3月22日（周五）下午16:00--17:00

报告地点：数理楼221

报告摘要：We consider an regularized mathematical program with equilibrium constraints (MPEC). The sparse solution selection from the solution set of convex programs and the second-order road pricing problem in transportation science can be modelled as this kind of problems. Due to the non-Lipschitzness of the regularization function, constraint qualifications for locally Lipschitz MPECs are no longer sufficient for Karush-Kuhn-Tucker (KKT) conditions to hold at a local minimizer. We first propose some qualification conditions and show that they are sufficient for KKT conditions to be necessary for optimality. Then we present a relaxed approximation method for solving this kind of problems where all the subproblems are more favorable compared with the original problem in the sense that the objective function is locally Lipschitz even smooth and the constraints typically satisfy certain constraint qualification. In our method, all the subproblems are solved until a weak approximate stationarity condition is satisfied. Due to the possible nonsmoothness of the objective function of the relaxed approximation subproblem, we also develop second-order necessary optimality for relaxed approximation subproblem. We show that any accumulation point of the sequence generated by our method is Clarke stationary if MPEC linear independence condition holds; it is Mordukhovich stationary if, in addition, an approaching subsequence satisfies an approximate weak second-order necessary condition; it is strongly stationary if, in addition, an upper level strict complementarity condition holds.