A strong convergence theorem for an iterative method for solving the split variational inequalities in Hilbert spaces
type: Item
instance of: scholarly article
title: A strong convergence theorem for an iterative method for solving the split variational inequalities in Hilbert spaces
zbMATH Open document ID: 1491.41012
author: Nguyen Thi Thu Thuy
published in: Vietnam Journal of Mathematics
publication date: 2021-12-03T00:00:00Z
review text: In this paper, a strong convergence theorem is given for the iteration of an algorithm to solve certain variational inequalities. The hypotheses are mild. These problems are called split variational inequalities. Not only the strong convergence result, but also the iterative method are new. The authors view this task as an optimization problem. The problem is a particularly difficult one, because one wishes to find a solution that satisfies certain inequalities which must be in a provided convex set and whose image by a linear operator is also in (another) given convex set, both at the same time. The operator is supposed to be bounded in order to make the mathematical problem feasible. The authors' algorithm is a modification of the well-known CQ algorithm which is essentially a projection gradient pursuit method.
Mathematics Subject Classification ID: 41A65
Mathematics Subject Classification ID: 47H20
zbMATH DE Number: 7438382
zbMATH Keywords: split variational inequality problems
zbMATH Keywords: split feasibility problems
zbMATH Keywords: multiple-sets problems
zbMATH Keywords: metric projection
reviewed by: Martin D. Buhmann
MaRDI profile type: Publication
full work available at URL: s10013-021-00476-w
OpenAlex ID: W3129347602
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DOI: 10.1007/S10013-021-00476-W
description: scientific article; zbMATH DE number 7438382