变分不等式和不动点问题的新迭代算法  

A New Iterative Method for Solving Variational Inequality and Fixed Point Problems

作　　者：郭丹妮 蔡钢 Dan Ni GUO(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,P.R.China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《数学学报（中文版）》2022年第1期77-88,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11771063,11971082);重庆市自然科学基金(cstc2020jcyj-msxmX0455);重庆市教委项目(KJZD-K201900504)。

摘　　要：本文在Hilbert空间上引入了一个新迭代算法,找到了伪单调变分不等式问题的解集与伪非扩张映射的不动点集的公共元.通过修改的超梯度算法,得到了弱收敛定理.所得结果推广和提高了许多最新结果.We introduce a new algorithm for solving pseudomonotone variational inequality problems and fixed point problems by using the subgradient extragradient method.A weak convergence theorem of proposed algorithm is obtained under some suitable assumptions imposed on the parameters.The results obtained in this paper extend and improve many recent ones in the literature.

关 键 词：伪单调算子 变分不等式 不动点 超梯度算法 

分 类 号：O177.91[理学—数学]