求解变分不等式问题和不动点问题公共点的惯性次梯度外梯度算法  

The Inertial Subgradient Extragradient Algorithm for Finding Common Elements of Variational Inequality Problems and Fixed Point Problems

作　　者：黄瑕 夏福全 张双德 HUANG Xia;XIA Fuquan;ZHANG Shuangde(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,Sichuan)

机构地区：[1]四川师范大学数学科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2021年第2期180-186,共7页Journal of Sichuan Normal University（Natural Science）

基　　金：教育部科学技术重点项目(212147)。

摘　　要：在Hilbert空间中提出一种新的惯性次梯度外梯度算法,求解具有单调Lipschitz连续映射的变分不等式问题的解集与非扩张映射的不动点集的公共点.该算法结合一般的次梯度外梯度算法和惯性算法.在一定的条件下,建立算法的弱收敛定理.数值实验结果表明,提出的算法有一定的意义.In this paper,we propose a new inertial subgradient extragradient algorithm,used to find the common elements of the fixed points set of a nonexpansive mapping and the set of solutions of a variational inequality problem for a monotone,Lipschitz-continuous mapping.The algorithm is a combination of the general subgradient extragradient algorithm and the inertial algorithm.Under certain conditions,we give the weak convergence theorem of the algorithm and give the numerical experiment to show that the proposed algorithm is of certain significance.

关 键 词：变分不等式 次梯度外梯度方法 惯性算法 弱收敛 

分 类 号：O177[理学—基础数学] O178