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运筹学学报 ›› 2011, Vol. 15 ›› Issue (4): 55-64.

• 运筹学 • 上一篇    下一篇

互补约束优化问题的乘子序列部分罚函数算法

刘水霞, 陈国庆   

  • 出版日期:2011-12-15 发布日期:2011-12-15

 A Multiplier Sequential Partial Penalization Algorithm for Mathematical Programs with Complementarity Constraints

 LIU  Shui-Xia, CHEN  Guo-Qing   

  • Online:2011-12-15 Published:2011-12-15

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被引次数

1

摘要： 利用互补问题的Lagrange函数,
将互补约束优化问题(MPCC)转化为含参数的约束优化问题.
给出Lagrange乘子的简单修正公式,
并给出求解互补约束优化问题的部分罚函数法. 无须假设二阶必要条件成立,
只要算法产生的迭代点列的极限点满足互补约束优化问题的线性独立约束规范(MPCC-LICQ),
且极限点是MPCC的可行点, 则算法收敛到原问题的M-稳定点. 另外,
在上水平严格互补(ULSC)成立的条件下, 算法收敛到原问题的B-稳定点.

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

Abstract: By using the Lagrangian function of the
complementarity problem, a mathematical program with complementarity
constraints (MPCC) is reformulated as a constrained optimization
problem with the multiplier parameter. The simple modified strategy
of the multiplier parameter is provided. Based on this, a multiplier
sequential partial penalization algorithm for MPCC
 is proposed. Without requiring the second-order necessary condition,
we show the limited point of the sequence (generated from the
algorithm) is an M-stationary point if it
 is the feasible to MPCC and the MPCC linear independence
 constraint qualification (LICQ) holds. Moreover, it
 is B-stationary point if
 the upper lever strict complementarity(ULSC) holds.

Key words: mathematical programs with complementarity constraints,  , Lagrangian function,  , upper lever strict complementarity, B-stationary point