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Article: An Accelerated Inexact Proximal Point Algorithm for Convex Minimization

TitleAn Accelerated Inexact Proximal Point Algorithm for Convex Minimization
Authors
KeywordsProximal point algorithm
Inexact
Convex minimization
Acceleration
Issue Date2012
Citation
Journal of Optimization Theory and Applications, 2012, v. 154, n. 2, p. 536-548 How to Cite?
AbstractThe proximal point algorithm is classical and popular in the community of optimization. In practice, inexact proximal point algorithms which solve the involved proximal subproblems approximately subject to certain inexact criteria are truly implementable. In this paper, we first propose an inexact proximal point algorithm with a new inexact criterion for solving convex minimization, and show its O(1/k) iteration-complexity. Then we show that this inexact proximal point algorithm is eligible for being accelerated by some influential acceleration schemes proposed by Nesterov. Accordingly, an accelerated inexact proximal point algorithm with an iteration-complexity of O(1/k 2 ) is proposed. © 2011 Springer Science+Business Media, LLC.
Persistent Identifierhttp://hdl.handle.net/10722/250998
ISSN
2020 Impact Factor: 2.249
2020 SCImago Journal Rankings: 1.109
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorHe, Bingsheng-
dc.contributor.authorYuan, Xiaoming-
dc.date.accessioned2018-02-01T01:54:17Z-
dc.date.available2018-02-01T01:54:17Z-
dc.date.issued2012-
dc.identifier.citationJournal of Optimization Theory and Applications, 2012, v. 154, n. 2, p. 536-548-
dc.identifier.issn0022-3239-
dc.identifier.urihttp://hdl.handle.net/10722/250998-
dc.description.abstractThe proximal point algorithm is classical and popular in the community of optimization. In practice, inexact proximal point algorithms which solve the involved proximal subproblems approximately subject to certain inexact criteria are truly implementable. In this paper, we first propose an inexact proximal point algorithm with a new inexact criterion for solving convex minimization, and show its O(1/k) iteration-complexity. Then we show that this inexact proximal point algorithm is eligible for being accelerated by some influential acceleration schemes proposed by Nesterov. Accordingly, an accelerated inexact proximal point algorithm with an iteration-complexity of O(1/k 2 ) is proposed. © 2011 Springer Science+Business Media, LLC.-
dc.languageeng-
dc.relation.ispartofJournal of Optimization Theory and Applications-
dc.subjectProximal point algorithm-
dc.subjectInexact-
dc.subjectConvex minimization-
dc.subjectAcceleration-
dc.titleAn Accelerated Inexact Proximal Point Algorithm for Convex Minimization-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1007/s10957-011-9948-6-
dc.identifier.scopuseid_2-s2.0-84864289740-
dc.identifier.volume154-
dc.identifier.issue2-
dc.identifier.spage536-
dc.identifier.epage548-
dc.identifier.eissn1573-2878-
dc.identifier.isiWOS:000306288300011-
dc.identifier.issnl0022-3239-

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