Iterative solution of unstable variational inequalities on approximately given sets
type: Item
instance of: scholarly article
title: Iterative solution of unstable variational inequalities on approximately given sets
zbMATH Open document ID: 0932.49014
DOI: 10.1155/S1085337596000024
author: Athanassios G. Kartsatos
author: Elena Litsyn
author: Yakov Alber
published in: Abstract and Applied Analysis
publication date: 2000-02-23T00:00:00Z
full work available at URL: https://eudml.org/doc/48352
full work available at URL: issue-1.html
review text: Summary: The convergence and the stability of the iterative regularization method for solving variational inequalities with bounded nonsmooth properly monotone (i.e., degenerate) operators in Banach spaces are studied. All the items of the inequality (i.e., the operator \(A\), the ``right-hand side'' \(f\) and the set of constraints \(\Omega\)) are to be perturbed. The connection between the parameters of regularization and perturbations which guarantee strong convergence of approximate solutions is established. In contrast to previous publications by Bruck, Reich and the first author, we do not suppose here that the approximating sequence is a priori bounded. Therefore the present results are new even for operator equations in Hilbert and Banach spaces. Apparently, the iterative processes for problems with perturbed sets of constraints are being considered for the first time.
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 47J20
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 47H05
Mathematics Subject Classification ID: 65L20
zbMATH DE Number: 1370665
zbMATH Keywords: convex sets
zbMATH Keywords: Lyapunov functionals
zbMATH Keywords: monotone operators
zbMATH Keywords: Hausdorff distances
zbMATH Keywords: convergence
zbMATH Keywords: stability
zbMATH Keywords: iterative regularization method
zbMATH Keywords: variational inequalities
zbMATH Keywords: perturbations
MaRDI profile type: Publication
OpenAlex ID: W2114161831
description: scientific article; zbMATH DE number 1370665