伪单调Non-Lipschitz算子的变分不等式问题的惯性黏性迭代方法  

Inertial Viscosity Iterative Method for Solving Variational Inequality Problems for Pseudo-monotone and Non-Lipschitz Operators

作　　者：蔡钢 刘丽亚 CAI Gang;LIU Liya(School of Mathematical Sciences,Chongqing Normal University,Chongqing,401331,P.R.China;School of Mathematical Sciences,University of Electronic Science and Technology of China,Chengdu,Sichuan,611731,P.R.China;School of Mathematics and Statistics,Southwest University,Chongqing,400715,P.R.China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331 [2]电子科技大学数学科学学院,成都四川611731 [3]西南大学数学与统计学院,重庆400715

出　　处：《数学进展》2022年第4期717-736,共20页Advances in Mathematics（China）

基　　金：Supported by NSFC (Nos.11771063,12171062);Natural Science Foundation of Chongqing(No.cstc2020jcyj-msxmX0455);Science and Technology Project of Chongqing Education Committee (No.KJZD-K201900504)。

摘　　要：本文在实Hilbert空间中引入求解伪单调non-Lipschitz连续算子的变分不等式问题的一种新的黏性超梯度算法.在对参数添加适当条件下得到了强收敛定理.还通过一些数值例子来支持我们的算法.主要结果推广和改进了一些相关的工作.The purpose of this paper is to propose a new viscosity extragradient algorithm for solving variational inequality problems of pseudo-monotone and non-Lipschitz continuous operators in real Hilbert spaces.Strong convergence theorems are given under some suitable conditions imposed on the parameters.We also give some numerical experiments to support our proposed algorithms.The main results obtained in this paper extend and improve some related works in the literature.

关 键 词：超梯度方法 变分不等式 黏性方法 伪单调算子 强收敛 

分 类 号：O177[理学—数学]