一种混合算法求解可分离带线性约束的变分不等式问题  

A MIXED ALGORITHM FOR SOLVING SEPARABLE VARIATIONAL INEQUALITIES WITH LINEAR CONSTRAINTS

作　　者：张从军[1] 李赛 吕丽霞[1] 王月虎[2] ZHANG Cong-jun;LI Sai;L?ULi-xia;WANG Yue-hu(School of Applied Mathematics,Nanjing University of Finance and Economics,Nanjing 210023,China;School of Management Science and Industrial Engineering,Nanjing University of Finance and Economics,Nanjing 210023,China)

机构地区：[1]南京财经大学应用数学学院, 江苏 南京 210023 [2]南京财经大学管理科学与工程学院, 江苏 南京 210023

出　　处：《数学杂志》2019年第2期234-248,共15页Journal of Mathematics

基　　金：江苏省高校自然科学研究面上项目(16KJB110009);江苏省自然科学基金(BK20171041);江苏高校哲学社会科学研究项目(2017SJB0238)

摘　　要：本文研究了大规模的可分离带线性约束的变分不等式问题,提出了基于对数二次临近点法的交替方向法,新算法的每步用一个非线性方程组来代替变分不等式子问题.通过有效求解非线性方程组,使得新算法简单易行而且一定程度上提高了计算的效率.同时,在映射单调和原问题解集非空的条件下,证明了此算法具有全局收敛性,最后通过数值实验说明了此算法是有效可行的.In this paper,we study large-scale separable variational inequality problem with linear constraints.Also,we propose a new alternating direction method which is based on the logarithmic-quadratic proximal method.By this method,we have nonlinear equations instead of sub-variational inequalities and it solves structural variational inequalities quickly.Meanwhile,mappings are monotonous and the solution set of the original problem is non-empty,we prove the new algorithm's global convergence,and the algorithm is effective and feasible.

关 键 词：变分不等式 交替方向法 全局收敛性 

分 类 号：O177.91[理学—数学]