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Article: Generalized alternating direction method of multipliers: new theoretical insights and applications

TitleGeneralized alternating direction method of multipliers: new theoretical insights and applications
Authors
KeywordsStatistical learning
Alternating direction method of multipliers
Convergence rate
Convex optimization
Discriminant analysis
Variable selection
Issue Date2015
Citation
Mathematical Programming Computation, 2015, v. 7, n. 2, p. 149-187 How to Cite?
Abstract© 2015, Springer-Verlag Berlin Heidelberg and The Mathematical Programming Society. Recently, the alternating direction method of multipliers (ADMM) has received intensive attention from a broad spectrum of areas. The generalized ADMM (GADMM) proposed by Eckstein and Bertsekas is an efficient and simple acceleration scheme of ADMM. In this paper, we take a deeper look at the linearized version of GADMM where one of its subproblems is approximated by a linearization strategy. This linearized version is particularly efficient for a number of applications arising from different areas. Theoretically, we show the worst-case $${\mathcal {O}}(1/k)$$O(1/k) convergence rate measured by the iteration complexity ($$k$$k represents the iteration counter) in both the ergodic and a nonergodic senses for the linearized version of GADMM. Numerically, we demonstrate the efficiency of this linearized version of GADMM by some rather new and core applications in statistical learning. Code packages in Matlab for these applications are also developed.
Persistent Identifierhttp://hdl.handle.net/10722/251101
ISSN
2020 SCImago Journal Rankings: 1.806
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorFang, Ethan X.-
dc.contributor.authorHe, Bingsheng-
dc.contributor.authorLiu, Han-
dc.contributor.authorYuan, Xiaoming-
dc.date.accessioned2018-02-01T01:54:34Z-
dc.date.available2018-02-01T01:54:34Z-
dc.date.issued2015-
dc.identifier.citationMathematical Programming Computation, 2015, v. 7, n. 2, p. 149-187-
dc.identifier.issn1867-2949-
dc.identifier.urihttp://hdl.handle.net/10722/251101-
dc.description.abstract© 2015, Springer-Verlag Berlin Heidelberg and The Mathematical Programming Society. Recently, the alternating direction method of multipliers (ADMM) has received intensive attention from a broad spectrum of areas. The generalized ADMM (GADMM) proposed by Eckstein and Bertsekas is an efficient and simple acceleration scheme of ADMM. In this paper, we take a deeper look at the linearized version of GADMM where one of its subproblems is approximated by a linearization strategy. This linearized version is particularly efficient for a number of applications arising from different areas. Theoretically, we show the worst-case $${\mathcal {O}}(1/k)$$O(1/k) convergence rate measured by the iteration complexity ($$k$$k represents the iteration counter) in both the ergodic and a nonergodic senses for the linearized version of GADMM. Numerically, we demonstrate the efficiency of this linearized version of GADMM by some rather new and core applications in statistical learning. Code packages in Matlab for these applications are also developed.-
dc.languageeng-
dc.relation.ispartofMathematical Programming Computation-
dc.subjectStatistical learning-
dc.subjectAlternating direction method of multipliers-
dc.subjectConvergence rate-
dc.subjectConvex optimization-
dc.subjectDiscriminant analysis-
dc.subjectVariable selection-
dc.titleGeneralized alternating direction method of multipliers: new theoretical insights and applications-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1007/s12532-015-0078-2-
dc.identifier.scopuseid_2-s2.0-84929327064-
dc.identifier.volume7-
dc.identifier.issue2-
dc.identifier.spage149-
dc.identifier.epage187-
dc.identifier.eissn1867-2957-
dc.identifier.isiWOS:000356018400002-
dc.identifier.issnl1867-2957-

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