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Article: Convergence rate analysis for the alternating direction method of multipliers with a substitution procedure for separable convex programming

TitleConvergence rate analysis for the alternating direction method of multipliers with a substitution procedure for separable convex programming
Authors
KeywordsConvergence rate
Iteration complexity
Convex programming
Contraction methods
Alternating direction method of multipliers
Issue Date2017
Citation
Mathematics of Operations Research, 2017, v. 42, n. 3, p. 662-691 How to Cite?
Abstract© 2017 INFORMS. Recently, in He et al. [He BS, Tao M, Yuan XM (2012) Alternating direction method with Gaussian back substitution for separable convex programming. SIAM J. Optim. 22(2):313-340], we have showed the first possibility of combining the Douglas- Rachford alternating direction method of multipliers (ADMM) with a Gaussian back substitution procedure for solving a convex minimization model with a general separable structure. This paper is a further study on this theme. We first derive a general algorithmic framework to combine ADMM with either a forward or backward substitution procedure. Then, we show that convergence of this framework can be easily proved from the contraction perspective, and its local linear convergence rate is provable if certain error bound condition is assumed. Without such an error bound assumption, we can estimate its worst-case convergence rate measured by the iteration complexity.
Persistent Identifierhttp://hdl.handle.net/10722/251234
ISSN
2020 Impact Factor: 2.008
2020 SCImago Journal Rankings: 1.619
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorHe, Bingsheng-
dc.contributor.authorTao, Min-
dc.contributor.authorYuan, Xiaoming-
dc.date.accessioned2018-02-01T01:54:58Z-
dc.date.available2018-02-01T01:54:58Z-
dc.date.issued2017-
dc.identifier.citationMathematics of Operations Research, 2017, v. 42, n. 3, p. 662-691-
dc.identifier.issn0364-765X-
dc.identifier.urihttp://hdl.handle.net/10722/251234-
dc.description.abstract© 2017 INFORMS. Recently, in He et al. [He BS, Tao M, Yuan XM (2012) Alternating direction method with Gaussian back substitution for separable convex programming. SIAM J. Optim. 22(2):313-340], we have showed the first possibility of combining the Douglas- Rachford alternating direction method of multipliers (ADMM) with a Gaussian back substitution procedure for solving a convex minimization model with a general separable structure. This paper is a further study on this theme. We first derive a general algorithmic framework to combine ADMM with either a forward or backward substitution procedure. Then, we show that convergence of this framework can be easily proved from the contraction perspective, and its local linear convergence rate is provable if certain error bound condition is assumed. Without such an error bound assumption, we can estimate its worst-case convergence rate measured by the iteration complexity.-
dc.languageeng-
dc.relation.ispartofMathematics of Operations Research-
dc.subjectConvergence rate-
dc.subjectIteration complexity-
dc.subjectConvex programming-
dc.subjectContraction methods-
dc.subjectAlternating direction method of multipliers-
dc.titleConvergence rate analysis for the alternating direction method of multipliers with a substitution procedure for separable convex programming-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1287/moor.2016.0822-
dc.identifier.scopuseid_2-s2.0-85026863168-
dc.identifier.volume42-
dc.identifier.issue3-
dc.identifier.spage662-
dc.identifier.epage691-
dc.identifier.eissn1526-5471-
dc.identifier.isiWOS:000407374800005-
dc.identifier.issnl0364-765X-

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