求解随机线性互补问题的Barzilai-Borwein算法  

Barzilai-Borwein Method for Solving Stochastic Linear Complementarity Problems

作　　者：魏潇[1] 

机构地区：[1]西安电子科技大学数学与统计学院,陕西西安710126

出　　处：《电子科技》2015年第2期7-10,共4页Electronic Science and Technology

基　　金：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)

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。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.

关 键 词：随机线性互补问题 Barzilai-Borwein算法 ERM模型 

分 类 号：O221.5[理学—运筹学与控制论]