A new relaxation method for mathematical programs with nonlinear complementarity constraints

作者：Li, Jianling; Huang, Xiaojin; Jian, Jinbao^*

来源：Journal of Computational Analysis and Applications, 2016, 20(3): 548-565.

• Nonlinear complementarity constraints
• Mathematical programs
• Relaxed method
• Constraint qualifications
• Stationary points
• Global convergence

In this paper, mathematical programs with nonlinear complementarity constraints (MPCC) are investigated and a new relaxed method is proposed. Firstly, based on Mangasarian complementarity function, MPCC is relaxed. The relaxed problem is a parametrized nonlinear programming. Secondly, it is proved that the sequence of stationary points of the relaxed problems converges to M-stationary point of MPCC under some mild assumptions; further, it is shown that the stationary point is strong for MPCC if some additional conditions are satisfied. Thirdly, we analyze the existence of the Lagrange multipliers for the relaxed problem. We show that Guignard constraint qualification holds for the relaxed problem under MPCC-linear independence constraint qualifications, and then obtain the existence theorem of the Lagrange multipliers.

• 出版日期2016-3
• 单位上海师范大学; 玉林师范学院; 广西大学