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Article: The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent

TitleThe direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent
Authors
KeywordsAlternating direction method of multipliers
Splitting methods
Convex programming
Convergence analysis
Issue Date2016
Citation
Mathematical Programming, 2016, v. 155, n. 1-2, p. 57-79 How to Cite?
Abstract© 2014, Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society. The alternating direction method of multipliers (ADMM) is now widely used in many fields, and its convergence was proved when two blocks of variables are alternatively updated. It is strongly desirable and practically valuable to extend the ADMM directly to the case of a multi-block convex minimization problem where its objective function is the sum of more than two separable convex functions. However, the convergence of this extension has been missing for a long time—neither an affirmative convergence proof nor an example showing its divergence is known in the literature. In this paper we give a negative answer to this long-standing open question: The direct extension of ADMM is not necessarily convergent. We present a sufficient condition to ensure the convergence of the direct extension of ADMM, and give an example to show its divergence.
Persistent Identifierhttp://hdl.handle.net/10722/251133
ISSN
2020 Impact Factor: 3.995
2020 SCImago Journal Rankings: 2.358
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorChen, Caihua-
dc.contributor.authorHe, Bingsheng-
dc.contributor.authorYe, Yinyu-
dc.contributor.authorYuan, Xiaoming-
dc.date.accessioned2018-02-01T01:54:42Z-
dc.date.available2018-02-01T01:54:42Z-
dc.date.issued2016-
dc.identifier.citationMathematical Programming, 2016, v. 155, n. 1-2, p. 57-79-
dc.identifier.issn0025-5610-
dc.identifier.urihttp://hdl.handle.net/10722/251133-
dc.description.abstract© 2014, Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society. The alternating direction method of multipliers (ADMM) is now widely used in many fields, and its convergence was proved when two blocks of variables are alternatively updated. It is strongly desirable and practically valuable to extend the ADMM directly to the case of a multi-block convex minimization problem where its objective function is the sum of more than two separable convex functions. However, the convergence of this extension has been missing for a long time—neither an affirmative convergence proof nor an example showing its divergence is known in the literature. In this paper we give a negative answer to this long-standing open question: The direct extension of ADMM is not necessarily convergent. We present a sufficient condition to ensure the convergence of the direct extension of ADMM, and give an example to show its divergence.-
dc.languageeng-
dc.relation.ispartofMathematical Programming-
dc.subjectAlternating direction method of multipliers-
dc.subjectSplitting methods-
dc.subjectConvex programming-
dc.subjectConvergence analysis-
dc.titleThe direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1007/s10107-014-0826-5-
dc.identifier.scopuseid_2-s2.0-84953209903-
dc.identifier.volume155-
dc.identifier.issue1-2-
dc.identifier.spage57-
dc.identifier.epage79-
dc.identifier.eissn1436-4646-
dc.identifier.isiWOS:000367695200002-
dc.identifier.issnl0025-5610-

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