Iterative methods for triple hierarchical variational inequalities in Hilbert spaces
type: Item
instance of: scholarly article
title: Iterative methods for triple hierarchical variational inequalities in Hilbert spaces
zbMATH Open document ID: 1262.90175
author: L. C. Ceng
author: Qamrul Hasan Ansari
author: Jen-Chih Yao
published in: Journal of Optimization Theory and Applications
publication date: 2012-02-13T00:00:00Z
review text: A variational inequality with a variational inequality constraint over a set of fixed points of a nonexpansive mapping is considered. Such a problem is called triple hierarchical variational inequality (THVI). Two iterative methods to compute approximate solutions of the problem are proposed: one is implicit and another one is explicit. This is carried out, for the first case, by combining the regularization, the hybrid steepest-descent, and the projection methods. For the second situation, a sequence via an iterative algorithm is generated, and it is proved that this sequence converges strongly to the unique solution of the THVI.
reviewed by: Fabián Flores-Bazan
Mathematics Subject Classification ID: 90C33
zbMATH DE Number: 6006028
zbMATH Keywords: triple hierarchical variational inequalities
zbMATH Keywords: iterative methods
zbMATH Keywords: implicit schemes
zbMATH Keywords: explicit schemes
zbMATH Keywords: fixed points
zbMATH Keywords: nonexpansive mappings
MaRDI profile type: Publication
full work available at URL: s10957-011-9882-7
OpenAlex ID: W1977720537
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DOI: 10.1007/S10957-011-9882-7
description: scientific article; zbMATH DE number 6006028