| 求解互补约束优化问题的乘子松弛法 |
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| 引用本文： | 刘水霞,陈国庆.求解互补约束优化问题的乘子松弛法[J].运筹学学报,2014,18(4):119-130. |
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| 作者姓名： | 刘水霞 陈国庆 |
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| 作者单位： | 1. 内蒙古大学数学科学学院, 呼和浩特 010021 |
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| 基金项目： | 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) |
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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.
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| 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 |
| 收稿时间： | 2014-04-18 |
A multiplier relaxation method for solving mathematical programs with complementarity constraints |
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| LIU Shuixia,CHEN Guoqing.A multiplier relaxation method for solving mathematical programs with complementarity constraints[J].OR Transactions,2014,18(4):119-130. |
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| Authors: | LIU Shuixia CHEN Guoqing |
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| Institution: | 1. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China |
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| Abstract: | 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. |
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| Keywords: | mathematical programs with complementarity constraints Lagrange function upper lever strict complementarity B-stationary point |
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