Finite convergence of algorithms for nonlinear programs and variational inequalities
type: Item
instance of: scholarly article
title: Finite convergence of algorithms for nonlinear programs and variational inequalities
zbMATH Open document ID: 0732.90076
DOI: 10.1007/BF00940629
author: Jerzy Kyparisis
author: Faiz Al-Khayyal
published in: Journal of Optimization Theory and Applications
publication date: 1991-01-01T00:00:00Z
review text: The authors derive a sufficient condition for nonlinear programs with convex feasible sets such that any convergent algorithm can be modified, by adding a convex subproblem with a linear objective function, to guarantee finite convergence in a generalized sense. When the feasible set is polyhedral, the subproblem is a linear program and finite convergence is obtained. Similar results are also developed for the variational inequality problem which calls for finding a point \(x'\in S\) such that \(G(x')^ T(x-x')\geq 0\), for all \(x\in S\), where G is a continuous mapping from \(R^ n\) to \(R^ n.\) Theorems 2.1 and 3.1 are two main results of the paper. In them, the assumption \(-\nabla f(x')\in int N(x')\) (resp., \(-G(x')\in int N(x'))\) is very crucial, where \(N(x')\) is the normal cone of the feasible set S at \(x'\).
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90-08
Mathematics Subject Classification ID: 49J40
zbMATH DE Number: 4211818
zbMATH Keywords: convergence analysis
zbMATH Keywords: convex feasible sets
zbMATH Keywords: variational inequality problem
reviewed by: Shouyang Wang
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00940629
OpenAlex ID: W2010413631
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description: scientific article; zbMATH DE number 4211818