Alternating direction method with self-adaptive penalty parameters for monotone variational inequalities
type: Item
instance of: scholarly article
title: Alternating direction method with self-adaptive penalty parameters for monotone variational inequalities
zbMATH Open document ID: 0997.49008
DOI: 10.1023/A:1004603514434
author: Hai Yang
author: S. L. Wang
author: Bingsheng He
published in: Journal of Optimization Theory and Applications
publication date: 2002-11-11T00:00:00Z
review text: In this paper the alternating direction method for solving linearly constrained separate monotone variational inequalities is studied. Experience on applications has shown that the number of the iterations depends significantly on the penalty parameter for the system of linear constraint equations. The main result of the paper is a convergence theorem for this method without any monotonicity assumption on the sequence of penalty parameters. This theorem applies to a modified alternating direction method that adjusts the penalty parameter per iteration based on the iterate message. Preliminary numerical tests are given to demonstrate the advantages of this self-adaptive adjustment technique.
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 90C33
Mathematics Subject Classification ID: 47J20
Mathematics Subject Classification ID: 90C59
zbMATH DE Number: 1558308
zbMATH Keywords: monotone variational inequalities
zbMATH Keywords: variable penalty parameter
zbMATH Keywords: alternating direction method
reviewed by: Walter Gómez Bofill
MaRDI profile type: Publication
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full work available at URL: a:1004603514434
OpenAlex ID: W1562101002
description: scientific article; zbMATH DE number 1558308