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浙江大学学报（理学版）
浙江大学学报（理学版）  2018, Vol. 45 Issue (2): 147-155    DOI: 10.3785/j.issn.1008-9497.2018.02.004
数学与计算机科学     
解互补约束优化问题的一种新的光滑化近似方法
申婷婷, 贺素香
武汉理工大学 理学院, 湖北 武汉 430070
A new smoothing method for mathematical programs with complementarity constraints
SHEN Tingting, HE Suxiang
Science College, Wuhan University of Technology, Wuhan 430070, China
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摘要： 互补约束优化问题应用十分广泛.利用Sigmoid函数的积分函数提出了一种新的光滑化近似算法，将互补约束优化问题转化为一般的非线性规划近似问题，通过求解近似问题的一系列光滑子问题得到原问题的近似解.在线性独立约束规范和其他一些较弱的假设条件下：无须上水平严格互补和渐进弱非退化，证明了光滑近似问题的KKT稳定点序列收敛于原问题的C-稳定点.进而考虑弱二阶必要条件，证明了上述KKT稳定点序列收敛于原问题的S-稳定点.最后，设计了相应算法，并对MacMPEC测试题库中的一些算例进行了数值实验，将得到的结果与其他算法的结果进行比较，显示本方法是有效的.
关键词： 线性独立约束规范;  C-稳定点;  S-稳定点;  互补约束优化问题    
Abstract: Mathematical programs with complementarity constraints (MPCC) have very wide application in many areas. In this paper, we present a smoothing method based on the integral of the Sigmoid function. The original MPCC is reformulated into a standard smooth optimization model. Then, we obtain an approximate solution of MPCC by solving a series of the smooth sub-problems. It is proved that any accumulation point of the KKT stationary points sequence is a C-stationary point of original MPCC under the linear independence constraints qualification (LICQ) and the other weaker assumptions, without upper level strict complementarity (ULSC) and asymptotically weakly nondegenerate condition (AWN). Furthermore, such an accumulation point can be proved to be S-stationary point under the weak second-order necessary condition. At last,we present the algorithm and test its efficiency with some problems in MacMPEC database. Numerical results indicate that the proposed smoothing method is efficient comparing with other related algorithms.
Key words: linear independence constraints qualification    C-stationary point    S-stationary point    mathematical programs with complementarity constraints
收稿日期: 2017-01-16 出版日期: 2018-03-08
CLC:  O221.2  
基金资助: 国家自然科学基金资助项目（11671183）.
通讯作者: 贺素香,ORCID:http://orcid.org/0000-0001-5800-9057,E-mail:hesux@whut.edu.cn     E-mail: hesux@whut.edu.cn
作者简介: 申婷婷(1992-),ORCID:http://orcid.org/0000-0001-6285-849X,女,硕士研究生,主要从事非线性优化理论与算法研究.
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引用本文:

申婷婷, 贺素香. 解互补约束优化问题的一种新的光滑化近似方法[J]. 浙江大学学报（理学版）, 2018, 45(2): 147-155.

SHEN Tingting, HE Suxiang. A new smoothing method for mathematical programs with complementarity constraints. Journal of ZheJIang University(Science Edition), 2018, 45(2): 147-155.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2018.02.004    或    https://www.zjujournals.com/sci/CN/Y2018/V45/I2/147

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