Decomposition method for a class of monotone variational inequality problems
type: Item
instance of: scholarly article
title: Decomposition method for a class of monotone variational inequality problems
zbMATH Open document ID: 0953.65049
DOI: 10.1023/A:1021736008175
author: Li-Zhi Liao
author: Hai Yang
author: Bingsheng He
published in: Journal of Optimization Theory and Applications
publication date: 2000-02-23T00:00:00Z
review text: A monotone variational inequality is considered on a set \(\Omega= X\times Y\), where \(X\) and \(Y\) are constraints sets. The classical augmented Lagrangian method is advantageous and effective when \(Y= \mathbb{R}^m\). For some problems of interest, such as minimax problems, where both \(X\) and \(Y\) are proper subsets in \(\mathbb{R}^n\) and \(\mathbb{R}^m\), the original augmented Lagrangian method is no longer applicable. A new decomposition method is introduced for that case and its convergence is demonstrated. If \(Y= \mathbb{R}^m\), the new method reduces to the augmented Lagrangian method. Numerical results for the new method are presented.
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 49M27
zbMATH DE Number: 1406366
zbMATH Keywords: numerical results
zbMATH Keywords: monotone variational inequality
zbMATH Keywords: minimax problems
zbMATH Keywords: decomposition method
zbMATH Keywords: convergence
zbMATH Keywords: augmented Lagrangian method
reviewed by: Viorel Arnăutu
MaRDI profile type: Publication
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full work available at URL: a:1021736008175
OpenAlex ID: W122578774
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description: scientific article; zbMATH DE number 1406366