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Article: Alternating direction method with Gaussian back substitution for separable convex programming

TitleAlternating direction method with Gaussian back substitution for separable convex programming
Authors
KeywordsGaussian back substitution
Convex programming
Separable structure
Alternating direction method
Issue Date2012
PublisherSociety for Industrial and Applied Mathematics. The Journal's web site is located at http://www.siam.org/journals/siopt.php
Citation
SIAM Journal on Optimization, 2012, v. 22, n. 2, p. 313-340 How to Cite?
AbstractWe consider the linearly constrained separable convex minimization problem whose objective function is separable into m individual convex functions with nonoverlapping variables. A Douglas-Rachford alternating direction method of multipliers (ADM) has been well studied in the literature for the special case of m = 2. But the convergence of extending ADM to the general case of m ≥ 3 is still open. In this paper, we show that the straightforward extension of ADM is valid for the general case of m ≥ 3 if it is combined with a Gaussian back substitution procedure. The resulting ADM with Gaussian back substitution is a novel approach towards the extension of ADM from m = 2 to m ≥ 3, and its algorithmic framework is new in the literature. For the ADM with Gaussian back substitution, we prove its convergence via the analytic framework of contractive-type methods, and we show its numerical efficiency by some application problems. © 2012 Society for Industrial and Applied Mathematics.
Persistent Identifierhttp://hdl.handle.net/10722/251004
ISSN
2020 Impact Factor: 2.85
2020 SCImago Journal Rankings: 2.066
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorHe, Bingsheng-
dc.contributor.authorTao, Min-
dc.contributor.authorYuan, Xiaoming-
dc.date.accessioned2018-02-01T01:54:18Z-
dc.date.available2018-02-01T01:54:18Z-
dc.date.issued2012-
dc.identifier.citationSIAM Journal on Optimization, 2012, v. 22, n. 2, p. 313-340-
dc.identifier.issn1052-6234-
dc.identifier.urihttp://hdl.handle.net/10722/251004-
dc.description.abstractWe consider the linearly constrained separable convex minimization problem whose objective function is separable into m individual convex functions with nonoverlapping variables. A Douglas-Rachford alternating direction method of multipliers (ADM) has been well studied in the literature for the special case of m = 2. But the convergence of extending ADM to the general case of m ≥ 3 is still open. In this paper, we show that the straightforward extension of ADM is valid for the general case of m ≥ 3 if it is combined with a Gaussian back substitution procedure. The resulting ADM with Gaussian back substitution is a novel approach towards the extension of ADM from m = 2 to m ≥ 3, and its algorithmic framework is new in the literature. For the ADM with Gaussian back substitution, we prove its convergence via the analytic framework of contractive-type methods, and we show its numerical efficiency by some application problems. © 2012 Society for Industrial and Applied Mathematics.-
dc.languageeng-
dc.publisherSociety for Industrial and Applied Mathematics. The Journal's web site is located at http://www.siam.org/journals/siopt.php-
dc.relation.ispartofSIAM Journal on Optimization-
dc.subjectGaussian back substitution-
dc.subjectConvex programming-
dc.subjectSeparable structure-
dc.subjectAlternating direction method-
dc.titleAlternating direction method with Gaussian back substitution for separable convex programming-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1137/110822347-
dc.identifier.scopuseid_2-s2.0-84865692854-
dc.identifier.volume22-
dc.identifier.issue2-
dc.identifier.spage313-
dc.identifier.epage340-
dc.identifier.isiWOS:000306100300003-
dc.identifier.issnl1052-6234-

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