There are no files associated with this item.

##### Supplementary
• Appears in Collections:

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

Title Generalized alternating direction method of multipliers: new theoretical insights and applications Fang, Ethan X.He, BingshengLiu, HanYuan, Xiaoming Statistical learningAlternating direction method of multipliersConvergence rateConvex optimizationDiscriminant analysisVariable selection 2015 Mathematical Programming Computation, 2015, v. 7, n. 2, p. 149-187 How to Cite? Â© 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. http://hdl.handle.net/10722/251101 1867-29492020 SCImago Journal Rankings: 1.806 WOS:000356018400002

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.abstractÂ© 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.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-