An explicit iterative algorithm for a class of variational inequalities in Hilbert spaces
type: Item
instance of: scholarly article
title: An explicit iterative algorithm for a class of variational inequalities in Hilbert spaces
zbMATH Open document ID: 1251.47059
author: Nguyen Buong
author: Lam Thuy Duong
published in: Journal of Optimization Theory and Applications
publication date: 2012-02-13T00:00:00Z
review text: Let \(H\) be a Hilbert space and let \(F\) be a strongly monotone Lipschitz-continuous nonlinear operator \(F:H\to{H}\). The problem under consideration is to find a point \(p^\ast\in{C}\) such that \(\langle{F}(p^\ast),\,p=p^\ast\rangle\geq0\) for every \(p\in{C}\). Here, \(C\subset{H}\) is a closed convex set of common fixed points of a finite family of nonexpansive maps \(T_i:H\to{H}\), \(i=1,2,\dots,N\). The authors propose an explicit iterative procedure generating a sequence which strongly converges to the unique solution of the variational inequality.
reviewed by: D. B. Silin
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47J20
zbMATH DE Number: 6006018
zbMATH Keywords: variational inequalities
zbMATH Keywords: Hilbert space
zbMATH Keywords: strong monotonicity
zbMATH Keywords: iterative algorithm
zbMATH Keywords: common fixed points
zbMATH Keywords: nonexpansive maps
MaRDI profile type: Publication
full work available at URL: s10957-011-9890-7
OpenAlex ID: W2086306319
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DOI: 10.1007/S10957-011-9890-7
description: scientific article; zbMATH DE number 6006018