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求解互补约束优化问题的乘子松弛法 被引量：1

A multiplier relaxation method for solving mathematical programs with complementarity constraints
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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.
作者 刘水霞 陈国庆
机构地区 内蒙古大学数学科学学院
出处 《运筹学学报》 CSCD 北大核心 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)
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 mathematical programs with complementarity constraints, Lagrangefunction, upper lever strict complementarity, B-stationary point
分类号 O221.2 [理学—运筹学与控制论]
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参考文献20

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二级参考文献17

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运筹学学报
2014年 第4期

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