A new iterative method for variational inequalities
type: Item
instance of: scholarly article
title: A new iterative method for variational inequalities
zbMATH Open document ID: 1110.65055
author: Abdellah Bnouhachem
author: Muhammad Aslam Noor
published in: Applied Mathematics and Computation
publication date: 2007-01-11T00:00:00Z
review text: The paper presents a new iterative method for variational inequalities. The solution of the elliptic variational inequality (by the projection technique) is equivalent to a fixed point problem. This alternative formulation has played a fundamental and significant part in developing several numerical methods for solving variational inequalities and related optimization problems. Since the convergence of these methods requires that the operator is both strongly monotone and Lipschitz continuous and as it is very difficult to evaluate the projection of the operator, the authors had to develop other techniques including the technique of updating of solution. Main results: A new iterative method is obtained by using three steps under suitable conditions. It is shown that the convergence of the proposed method requires only pseudomonotonicity. The new method is globally convergent. Finally an example is presented to illustrate the efficiency and advantage of the proposed new iterative method.
Mathematics Subject Classification ID: 65K10
zbMATH DE Number: 5115437
zbMATH Keywords: elliptic variational inequality
zbMATH Keywords: iterative method
zbMATH Keywords: projection operator
zbMATH Keywords: fixed point problem
zbMATH Keywords: strongly monotone and Lipschitz continuous operator
zbMATH Keywords: convergence
zbMATH Keywords: algorithm
zbMATH Keywords: numerical example
reviewed by: Jan Lovíšek
MaRDI profile type: Publication
full work available at URL: j.amc.2006.06.007
OpenAlex ID: W2025273234
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DOI: 10.1016/J.AMC.2006.06.007
description: scientific article; zbMATH DE number 5115437