Modified self-adaptive projection method for solving pseudomonotone variational inequalities
type: Item
instance of: scholarly article
title: Modified self-adaptive projection method for solving pseudomonotone variational inequalities
zbMATH Open document ID: 1221.65157
author: Zeng Yu
author: Hu Shao
author: Guodong Wang
published in: Applied Mathematics and Computation
publication date: 2011-06-28T00:00:00Z
review text: The authors consider the following variational inequality problem: \[ \text{Find a vector }x'\in\Omega, \text{ such that }(x- x^*)F(x^*)\geq 0,\;\forall x\in\Omega, \] where \(\Omega\) is assumed to be a nonempty closed convex subset of \(\mathbb{R}^n\); \(F\) is assumed to be a mapping from \(\mathbb{R}^n\) into itself. For this variational inequality, a self-adaptive projection method with a new search direction is proposed. The descent property of the new search direction is proved, which is useful to guarantee the convergence. Under the relatively relaxed condition that \(F\) is continuous and pseudomonotone, the global convergence of the method is proved. Computational results are presented.
reviewed by: Hans Benker
Mathematics Subject Classification ID: 65K15
zbMATH DE Number: 5914118
zbMATH Keywords: pseudomonotone
zbMATH Keywords: variational inequalities
zbMATH Keywords: self-adaptive
zbMATH Keywords: projection methods
zbMATH Keywords: global convergence
MaRDI profile type: Publication
full work available at URL: j.amc.2011.03.004
OpenAlex ID: W2122104076
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DOI: 10.1016/J.AMC.2011.03.004
description: scientific article; zbMATH DE number 5914118