Applications of fixed-point methods to discrete variational and quasi- variational inequalities
type: Item
instance of: scholarly article
title: Applications of fixed-point methods to discrete variational and quasi- variational inequalities
zbMATH Open document ID: 0613.65070
DOI: 10.1007/BF01400174
author: S. A. Belbas
author: Isaak Mayergoyz
published in: Numerische Mathematik
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133218
review text: Discrete analogues of variational inequalities (VI) and quasi-variational inequalities (QVI), encountered in stochastic control and mathematical physics, are discussed. It is shown that those discrete VI's and QVI's can be written in the fixed point form \(x=Tx\) such that either T or some power of T is a contraction. This leads to globally convergent iterative methods for the solution of discret VI's and QVI's, which are very suitable for implementation on parallel computers with single- instruction, multiple-data architecture, particularly on massive parallel processors.
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 49M25
zbMATH DE Number: 3992829
zbMATH Keywords: fixed-point methods
zbMATH Keywords: quasi-variational inequalities
zbMATH Keywords: stochastic control
zbMATH Keywords: iterative methods
zbMATH Keywords: parallel processors
zbMATH Keywords: finite-difference approximation
zbMATH Keywords: contraction mapping
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3992829