Augmented Lagrangian theory, duality and decomposition methods for variational inequality problems
type: Item
instance of: scholarly article
title: Augmented Lagrangian theory, duality and decomposition methods for variational inequality problems
zbMATH Open document ID: 1046.49008
DOI: 10.1023/A:1023664709604
author: D. Massart
published in: Journal of Optimization Theory and Applications
publication date: 2003-10-29T00:00:00Z
review text: The paper is devoted to extension of the augmented Lagrangian theory from convex optimization problems to constrained variational inequalities. Based on these results, the author presents a multiplier method for variational inequalities. It should be noted that similar results have been obtained by \textit{A.~Auslender and M.~Teboulle} [SIAM J. Optim., 10, No. 4, 1097--1115 (2000; Zbl 0996.49005)] and by \textit{I.V.~Konnov} [Comput. Math. Math. Phys., 41, No. 9, 1279--1291 (2001); translation from Zh. Vychisl. Mat. Mat. Fiz. 41, No. 9, 1344--1357 (2001; Zbl 1022.49008) and Optimization 51, No. 6, 907--926 (2002; Zbl 1022.49007)]. A decomposable variant of the Arrow-Hurwicz type method with the augmented Lagrangian is also presented.
reviewed by: Igor V. Konnov
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 90C46
Mathematics Subject Classification ID: 49M27
zbMATH DE Number: 1997755
zbMATH Keywords: variational inequalities
zbMATH Keywords: augmented Lagrangians
zbMATH Keywords: decomposition
MaRDI profile type: Publication
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full work available at URL: a:1023664709604
OpenAlex ID: W166252871
description: scientific article; zbMATH DE number 1997755