求解互补约束优化问题的松弛法  

A Relaxation Method for Mathematical Programs with Complementarity Constraints

作　　者：刘水霞[1] 陈国庆[1] 

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021

出　　处：《内蒙古大学学报（自然科学版）》2008年第6期620-627,共8页Journal of Inner Mongolia University：Natural Science Edition

基　　金：高等学校骨干教师资助计划项目;内蒙古自治区优秀学科带头人资助项目

摘　　要：给出求解互补约束优化问题(MPCC)的松弛法,并研究其松弛问题的稳定点的收敛性质.在MPCC-LICQ的条件下,松弛问题的稳定点的任何聚点都是原问题的C-稳定点.若松弛问题的Lagrange函数的Hessian矩阵在相应的切空间一致下有界,则聚点是M-稳定点.若Hessian矩阵的最小特征值有界,则聚点是B-稳定点.A relaxation method for mathematical program with complementarity constraints is given. The convergence behavior of a sequence of stationary points of the relaxed problems is considered. Any accumulation point of stationary points of relaxed problems is C-stationary point of MPCC under MPCC linear indenpendence constraint qualification,and if the Hessian matrices of the Lagrangian functions of the relaxed problems are uniformly bounded below on the corresponding tangent space, it is M-stationary. Moreover if the small eigenvalue of the Hessian matrices is bounded below,it is B-stationary.

关 键 词：互补约束优化问题 B-稳定点 弱二阶必要条件 

分 类 号：O221.2[理学—运筹学与控制论]