非单调光滑牛顿算法求解随机广义线性互补问题  

Nonmonotone Smoothing Newton Method for Solving Stochastic Generalized Linear Complementarity Problem

作　　者：张静 张颖 Zhang Jing;Zhang Ying({School of Mathematics,Tianjin University,Tianjin 300072,China)

机构地区：[1]天津大学数学学院,天津300072

出　　处：《南开大学学报（自然科学版）》2020年第2期29-37,共9页Acta Scientiarum Naturalium Universitatis Nankaiensis

基　　金：Supported by Nature Science Foundation of China(11471241)。

摘　　要：研究了一类含有有限个离散型随机变量的随机广义线性互补问题的数值求解方法.利用期望均值重构和对称扰动的互补函数,将该问题重构成光滑方程组,并提出了一种具有新的非单调线搜索的光滑牛顿算法用来求解重构后问题.在一定条件下,此算法是全局收敛的,且其收敛速度是局部二次的.A class of stochastic generalized linear complementarity problems with finitely many realizations is studied. Based on Expected value formulation and smoothing symmetric perturbed Fischer function,the stochastic generalized linear complementarity problems are reformulated as a system of smoothing equations. Then, a smoothing Newton method with nonmonotone line search strategy is presented to solve the new formulation. Moreover, it’s proved that this nonmonotone smoothing algorithm is globally and local quadratically convergent under suitable assumptions.

关 键 词：随机广义线性互补问题 期望均值重构 光滑牛顿算法 非单调线搜索 

分 类 号：O224[理学—运筹学与控制论]