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Article: A proximal point algorithm revisit on the alternating direction method of multipliers

TitleA proximal point algorithm revisit on the alternating direction method of multipliers
Authors
Keywordsalternating direction method of multipliers
proximal point algorithm
convex programming
convergence rate
Issue Date2013
Citation
Science China Mathematics, 2013, v. 56, n. 10, p. 2179-2186 How to Cite?
AbstractThe alternating direction method of multipliers (ADMM) is a benchmark for solving convex programming problems with separable objective functions and linear constraints. In the literature it has been illustrated as an application of the proximal point algorithm (PPA) to the dual problem of the model under consideration. This paper shows that ADMM can also be regarded as an application of PPA to the primal model with a customized choice of the proximal parameter. This primal illustration of ADMM is thus complemental to its dual illustration in the literature. This PPA revisit on ADMM from the primal perspective also enables us to recover the generalized ADMM proposed by Eckstein and Bertsekas easily. A worst-case O(1/t) convergence rate in ergodic sense is established for a slight extension of Eckstein and Bertsekas's generalized ADMM. © 2013 Science China Press and Springer-Verlag Berlin Heidelberg.
Persistent Identifierhttp://hdl.handle.net/10722/250875
ISSN
2020 Impact Factor: 1.331
2020 SCImago Journal Rankings: 0.818
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorCai, Xing Ju-
dc.contributor.authorGu, Guo Yong-
dc.contributor.authorHe, Bing Sheng-
dc.contributor.authorYuan, Xiao Ming-
dc.date.accessioned2018-02-01T01:53:57Z-
dc.date.available2018-02-01T01:53:57Z-
dc.date.issued2013-
dc.identifier.citationScience China Mathematics, 2013, v. 56, n. 10, p. 2179-2186-
dc.identifier.issn1674-7283-
dc.identifier.urihttp://hdl.handle.net/10722/250875-
dc.description.abstractThe alternating direction method of multipliers (ADMM) is a benchmark for solving convex programming problems with separable objective functions and linear constraints. In the literature it has been illustrated as an application of the proximal point algorithm (PPA) to the dual problem of the model under consideration. This paper shows that ADMM can also be regarded as an application of PPA to the primal model with a customized choice of the proximal parameter. This primal illustration of ADMM is thus complemental to its dual illustration in the literature. This PPA revisit on ADMM from the primal perspective also enables us to recover the generalized ADMM proposed by Eckstein and Bertsekas easily. A worst-case O(1/t) convergence rate in ergodic sense is established for a slight extension of Eckstein and Bertsekas's generalized ADMM. © 2013 Science China Press and Springer-Verlag Berlin Heidelberg.-
dc.languageeng-
dc.relation.ispartofScience China Mathematics-
dc.subjectalternating direction method of multipliers-
dc.subjectproximal point algorithm-
dc.subjectconvex programming-
dc.subjectconvergence rate-
dc.titleA proximal point algorithm revisit on the alternating direction method of multipliers-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1007/s11425-013-4683-0-
dc.identifier.scopuseid_2-s2.0-84884416593-
dc.identifier.volume56-
dc.identifier.issue10-
dc.identifier.spage2179-
dc.identifier.epage2186-
dc.identifier.isiWOS:000324514200018-
dc.identifier.issnl1869-1862-

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