Convergence analysis of iterative methods for some variational inequalities with pseudomonotone operators
type: Item
instance of: scholarly article
title: Convergence analysis of iterative methods for some variational inequalities with pseudomonotone operators
zbMATH Open document ID: 1010.47041
DOI: 10.1023/A:1011901503460
author: O. A. Zadvornov
author: A. M. Saddek
author: I. B. Badriyev
published in: Differential Equations
publication date: 2003-05-18T00:00:00Z
review text: The authors consider variational inequalities of the second kind with a pseudomonotone operator and a convex nondifferentiable functional in Banach spaces. A two-layer iterative method is proposed for solvability, which reduces the original variational inequality to one with a duality operator that has better properties than the original operator. The convergence of the iterative process is analyzed. In particular, it is shown that the iterative sequence is bounded and each of its weak limit point is a solution of the original inequality. In the case of a Hilbert space, weak convergence is proved of the entire iterative sequence under suitable additional requirements.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 47J20
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 49J40
zbMATH DE Number: 1758768
zbMATH Keywords: variational inequalities
zbMATH Keywords: pseudomonotone mappings
zbMATH Keywords: iterative methods
MaRDI profile type: Publication
full work available at URL: a:1011901503460
OpenAlex ID: W215213336
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description: scientific article; zbMATH DE number 1758768