一类变分不等式的随机步长收缩算法  

Stochastic Steplength Contraction Method for a Class of Variational Inequalities

作　　者：徐海文[1,2] 

机构地区：[1]南京航空航天大学民航学院,南京210016 [2]中国民航飞行学院计算机学院,四川广汉618307

出　　处：《工程数学学报》2011年第4期461-469,共9页Chinese Journal of Engineering Mathematics

基　　金：国家科技支撑项目(2011BAH24B06);中国民航飞行学院科研基金(J2010-45)~~

摘　　要：最近何炳生提出了一类变分不等式的改善步长收缩算法(E-Method).然而,该算法的收敛性证明表明了E-Method的固定扩张步长没有充分利用下降量函数的不等式放缩.本文利用服从高斯分布的随机数来随机扩张步长,得到了变分不等式的随机步长收缩算法(SC-Method),克服了E-Method固定扩张步长的缺点.同时在适当的条件下,给出了收敛性证明.通过对来自于金融和统计中的一类变分不等式问题的一系列数值试验,验证了SC-Method的高效性.The extended contraction method （E-Method） proposed by He is an effective method for a class of variational inequalities. However, the convergence analysis of E-Method indicates that the inequalities in dropping function are not fully employed when the steplength extension is fixed. In this paper, we propose the stochastic steplength contraction method （SC-Method） for a class of variational inequalities through the random steplength extension based the random variable generated from the Gaussian distribution. The SC-Method also ameliorates the issue of fixed steplength extension existed in the E-Method. Meanwhile, the convergence of SC-Method is proved under suitable conditions. It should also be noted that the efficiency of SC-Method is confirmed through a series of numerical experiments originated from finance and statistics.

关 键 词：收缩算法 变分不等式 随机分布 邻近点算法 交替方向法 

分 类 号：O221[理学—运筹学与控制论]