求解随机线性互补问题的Barzilai-Borwein算法

›› 2015, Vol. 28 ›› Issue (2): 7-.

求解随机线性互补问题的Barzilai-Borwein算法

魏潇

(西安电子科技大学数学与统计学院,陕西西安 710126)

出版日期:2015-02-15 发布日期:2015-02-16
作者简介:魏潇(1991—),女,硕士研究生。研究方向:随机互补理论和算法。E-mail:weixiao4256@126.com
基金资助:
国家自然科学基金资助项目(61072144;61179040);中央高校基本科研业务费专项基金资助项目(K50513100007)

Barzilai-Borwein Method for Solving Stochastic Linear Complementarity Problems

WEI Xiao

(School of Mathematics and Statistics,Xidian University,Xi'an 710126,China)

Online:2015-02-15 Published:2015-02-16

摘要/Abstract

摘要：

随机线性互补是一类特殊的互补问题。常用的求解方法是先将其转化为约束极小化模型,然后用优化算法求解该模型。文中针对随机线性互补问题的期望残差极小化模型,通过使用Barzilai-Borwein步和有效集策略,提出了求解该模型的Barzilai-Borwein算法。实验结果表明,该算法与光滑投影梯度法相比,能在更短的时间内得到相应的数值结果。

关键词: 随机线性互补问题, Barzilai-Borwein算法, ERM模型

Abstract:

As a special kind of complementarity problem,stochastic linear complementarity is considered.The common method for the problem is to reformulate it as a constrained minimization problem,and then solve the minimization problem by the optimized algorithm.In this paper,we study the expected residual minimization reformulation of the stochastic linear complementarity problem.By employing the Barzilai-Borwein step size and active set strategy,a Barzilai-Borwein type method is proposed to solve this reformulation.Numerical experiments confirm that compared with the smooth projected gradient Newton method,the new method can get numerical results with less time.

Key words: stochastic linear complementarity;Barzilai-Borwein method;ERM reformulation

中图分类号:

O221.5

魏潇. 求解随机线性互补问题的Barzilai-Borwein算法[J]. , 2015, 28(2): 7-.

WEI Xiao. Barzilai-Borwein Method for Solving Stochastic Linear Complementarity Problems[J]. , 2015, 28(2): 7-.

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