求解互补约束优化问题的乘子松弛法  

A multiplier relaxation method for solving 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：《运筹学学报》2014年第4期119-130,共12页Operations Research Transactions

基　　金：国家自然科学基金(No.11261033);内蒙古大学高层次人才引进科研启动基金(No.210143)

摘　　要：利用互补问题的Lagrange函数,给出了互补约束优化问题(MPCC)的一种新松弛问题.在较弱的条件下,新松弛问题满足线性独立约束规范.在此基础上,提出了求解互补约束优化问题的乘子松弛法.在MPCC-LICQ条件下,松弛问题稳定点的任何聚点都是MPCC的M-稳定点.无需二阶必要条件,只在ULSC条件下,就可保证聚点是MPCC的B-稳定点.另外,给出了算法收敛于B-稳定点的新条件.By using the Lagrange function of the complementarity problem, a new relaxed problem of MPCC is given. We show that the linear independence constraint qualification holds for the new relaxed problem under some mild conditions. Based on this, a multiplier relaxed method for solving MPCC is presented. The limited point of stationary points of the relaxed problems is M-stationary point under the MPCC-LICQ. Without requiring the second-order necessary condition, the limited point is B-stationary point if the ULSC holds. At last, we propose a new condition for convergence to B- stationary point.

关 键 词：互补约束优化问题 LAGRANGE函数 上水平严格互补 B-稳定点 

分 类 号：O221.2[理学—运筹学与控制论]