Convergence of the Modified Extragradient Method for Variational Inequalities with Non-Lipschitz Operators

被引：155

作者：

Denisov S.V. ^{[1
]}

Semenov V.V. ^{[1
]}

Chabak L.M. ^{[2
]}

机构：

[1] Taras Shevchenko National University of Kyiv, Kyiv

[2] Hetman Konashevych-Sahaidachnyi Kyiv State Maritime Academy, Kyiv

来源：

Cybernetics and Systems Analysis | 2015年 / 51卷 / 05期

关键词：

extragradient method; Hilbert space; monotone operator; variational inequality; weak convergence;

D O I：

10.1007/s10559-015-9768-z

中图分类号：

学科分类号：

摘要：

We propose a modified extragradient method with dynamic step size adjustment to solve variational inequalities with monotone operators acting in a Hilbert space. In addition, we consider a version of the method that finds a solution of a variational inequality that is also a fixed point of a quasi-nonexpansive operator. We establish the weak convergence of the methods without any Lipschitzian continuity assumption on operators. © 2015, Springer Science+Business Media New York.

引用

页码：757 / 765

页数：8

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