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Article: Linearized alternating direction method of multipliers with Gaussian back substitution for separable convex programming

TitleLinearized alternating direction method of multipliers with Gaussian back substitution for separable convex programming
Authors
KeywordsAlternating direction method of multipliers
Separable convex programming
Resolvent operator
Linearization
Gaussian back substitution
Issue Date2013
Citation
Numerical Algebra, Control and Optimization, 2013, v. 3, n. 2, p. 247-260 How to Cite?
AbstractRecently, we have proposed combining the alternating direction method of multipliers (ADMM) with a Gaussian back substitution procedure for solving the convex minimization model with linear constraints and a general separable objective function, i.e., the objective function is the sum of many functions without coupled variables. In this paper, we further study this topic and show that the decomposed subproblems in the ADMM procedure can be substantially alleviated by linearizing the involved quadratic terms arising from the augmented Lagrangian penalty. When the resolvent operators of the separable functions in the objective have closed-form representations, embedding the linearization into the ADMM subproblems becomes necessary to yield easy subproblems with closed-form solutions. We thus show theoretically that the blend of ADMM, Gaussian back substitution and linearization works effectively for the separable convex minimization model under consideration.
Persistent Identifierhttp://hdl.handle.net/10722/251058
ISSN
2023 Impact Factor: 1.1
2023 SCImago Journal Rankings: 0.385
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorHe, Bingsheng-
dc.contributor.authorYuan, Xiaoming-
dc.date.accessioned2018-02-01T01:54:27Z-
dc.date.available2018-02-01T01:54:27Z-
dc.date.issued2013-
dc.identifier.citationNumerical Algebra, Control and Optimization, 2013, v. 3, n. 2, p. 247-260-
dc.identifier.issn2155-3289-
dc.identifier.urihttp://hdl.handle.net/10722/251058-
dc.description.abstractRecently, we have proposed combining the alternating direction method of multipliers (ADMM) with a Gaussian back substitution procedure for solving the convex minimization model with linear constraints and a general separable objective function, i.e., the objective function is the sum of many functions without coupled variables. In this paper, we further study this topic and show that the decomposed subproblems in the ADMM procedure can be substantially alleviated by linearizing the involved quadratic terms arising from the augmented Lagrangian penalty. When the resolvent operators of the separable functions in the objective have closed-form representations, embedding the linearization into the ADMM subproblems becomes necessary to yield easy subproblems with closed-form solutions. We thus show theoretically that the blend of ADMM, Gaussian back substitution and linearization works effectively for the separable convex minimization model under consideration.-
dc.languageeng-
dc.relation.ispartofNumerical Algebra, Control and Optimization-
dc.subjectAlternating direction method of multipliers-
dc.subjectSeparable convex programming-
dc.subjectResolvent operator-
dc.subjectLinearization-
dc.subjectGaussian back substitution-
dc.titleLinearized alternating direction method of multipliers with Gaussian back substitution for separable convex programming-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.3934/naco.2013.3.247-
dc.identifier.scopuseid_2-s2.0-84892589055-
dc.identifier.volume3-
dc.identifier.issue2-
dc.identifier.spage247-
dc.identifier.epage260-
dc.identifier.eissn2155-3297-
dc.identifier.isiWOS:000214964800006-
dc.identifier.issnl2155-3297-

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