求解垂直互补约束数学规划问题的松弛方法(英文)

Relaxation Method for Mathematical Programs with Vertical Complementarity Constraints

垂直互补约束数学规划问题在工程设计、生产计划、优化控制等方面有很多应用.本文提出了一种求解垂直互补约束数学规划问题的松弛方法,并证明了:在垂直互补约束数学规划问题线性独立的约束规范条件下,松弛问题稳定点的任何聚点是原问题的C-稳定点.如果进一步还满足二阶必要性条件,则这些聚点是M-稳定点.基本数值结果表明提出的方法可以很好的求解垂直互补约束数学规划问题.

Mathematical program with vertical complementarity constraints （MPVCC） has many applications in various fields such as engineering design, manufacturing plan, optimal control and mathematical programming itself. We present a relaxation method for MPVCC. We show that, under the MPVCC linear independence constraint qualification, any limiting point of stationary points of the relaxed problems is Clarke stationary to the original problem and, if the additional second order necessary optimality conditions are satisfied, the limiting points must be M-stationary. Preliminary numerical results show that the proposed method is able to finely solve MPVCC.