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Article: Further Study on the Convergence Rate of Alternating Direction Method of Multipliers with Logarithmic-quadratic Proximal Regularization

TitleFurther Study on the Convergence Rate of Alternating Direction Method of Multipliers with Logarithmic-quadratic Proximal Regularization
Authors
KeywordsLogarithmic-quadratic proximal
Convergence rate
Convex programming
Iteration complexity
Alternating direction method of multipliers
Issue Date2015
Citation
Journal of Optimization Theory and Applications, 2015, v. 166, n. 3, p. 906-929 How to Cite?
Abstract© 2014, Springer Science+Business Media New York. In the literature, the combination of the alternating direction method of multipliers with the logarithmic-quadratic proximal regularization has been proved to be convergent, and its worst-case convergence rate in the ergodic sense has been established. In this paper, we focus on a convex minimization model and consider an inexact version of the combination of the alternating direction method of multipliers with the logarithmic-quadratic proximal regularization. Our primary purpose is to further study its convergence rate and to establish its worst-case convergence rates measured by the iteration complexity in both the ergodic and non-ergodic senses. In particular, existing convergence rate results for this combination are subsumed by the new results.
Persistent Identifierhttp://hdl.handle.net/10722/251115
ISSN
2023 Impact Factor: 1.6
2023 SCImago Journal Rankings: 0.864
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorChen, Caihua-
dc.contributor.authorLi, Min-
dc.contributor.authorYuan, Xiaoming-
dc.date.accessioned2018-02-01T01:54:37Z-
dc.date.available2018-02-01T01:54:37Z-
dc.date.issued2015-
dc.identifier.citationJournal of Optimization Theory and Applications, 2015, v. 166, n. 3, p. 906-929-
dc.identifier.issn0022-3239-
dc.identifier.urihttp://hdl.handle.net/10722/251115-
dc.description.abstract© 2014, Springer Science+Business Media New York. In the literature, the combination of the alternating direction method of multipliers with the logarithmic-quadratic proximal regularization has been proved to be convergent, and its worst-case convergence rate in the ergodic sense has been established. In this paper, we focus on a convex minimization model and consider an inexact version of the combination of the alternating direction method of multipliers with the logarithmic-quadratic proximal regularization. Our primary purpose is to further study its convergence rate and to establish its worst-case convergence rates measured by the iteration complexity in both the ergodic and non-ergodic senses. In particular, existing convergence rate results for this combination are subsumed by the new results.-
dc.languageeng-
dc.relation.ispartofJournal of Optimization Theory and Applications-
dc.subjectLogarithmic-quadratic proximal-
dc.subjectConvergence rate-
dc.subjectConvex programming-
dc.subjectIteration complexity-
dc.subjectAlternating direction method of multipliers-
dc.titleFurther Study on the Convergence Rate of Alternating Direction Method of Multipliers with Logarithmic-quadratic Proximal Regularization-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1007/s10957-014-0682-8-
dc.identifier.scopuseid_2-s2.0-84938414458-
dc.identifier.volume166-
dc.identifier.issue3-
dc.identifier.spage906-
dc.identifier.epage929-
dc.identifier.eissn1573-2878-
dc.identifier.isiWOS:000358744000011-
dc.identifier.issnl0022-3239-

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