On the use of regularization to correct monotone variational inequalities given approximately
type: Item
instance of: scholarly article
title: On the use of regularization to correct monotone variational inequalities given approximately
zbMATH Open document ID: 0811.47068
published in: Russian Mathematics
publication date: 1994-02-13T00:00:00Z
review text: This article deals with Browder-Tikhonov regularization in application to the variational inequality \[ \langle Fx- f, x-z\rangle\leq 0 \qquad (z\in Q) \tag \(*\) \] where \(F\) is a monotone operator acting from \(D(P) \subseteq \mathbb{X}\) into \(\mathbb{X}^*\), \(\mathbb{X}\) is a strictly convex Banach space with strictly convex conjugate space \(\mathbb{X}^*\) in the case when the solution set of \((*)\) is empty. The main result is a theorem about conditions under which the Browder-Tikhonov regularization defines the solution to the variational inequality \[ \langle Fx- f+v_ *, x-z\rangle \leq 0 \qquad (z\in Q) \tag \(**\) \] with the least \(v_ *\in \mathbb{X}^*\); further a theorem about conditions under which the finite-dimensional approximations of the Browder-Tikhonov regularization define the solution to \((**)\). As an example the elliptic variational inequality of second order of the Dirichlet problem is considered in detail.
Mathematics Subject Classification ID: 47J20
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 35J20
zbMATH DE Number: 484321
zbMATH Keywords: Browder-Tikhonov regularization
zbMATH Keywords: variational inequality
zbMATH Keywords: monotone operator
zbMATH Keywords: strictly convex Banach space
zbMATH Keywords: strictly convex conjugate space
zbMATH Keywords: finite-dimensional approximation of the Browder-Tikhonov regularization
zbMATH Keywords: elliptic variational inequality of second order of the Dirichlet problem
author: Mikhail Yu. Kokurin
reviewed by: Peter P. Zabreĭko
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 484321