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Article: Convergence analysis of primal-dual algorithms for a saddle-point problem: From contraction perspective

TitleConvergence analysis of primal-dual algorithms for a saddle-point problem: From contraction perspective
Authors
KeywordsTotal variation
Proximal point algorithm
Primal-dual method
Image restoration
Contraction method
Saddle point problem
Issue Date2012
PublisherSociety for Industrial and Applied Mathematics. The Journal's web site is located at http://www.siam.org/journals/siims.php
Citation
SIAM Journal on Imaging Sciences, 2012, v. 5, n. 1, p. 119-149 How to Cite?
AbstractRecently, some primal-dual algorithms have been proposed for solving a saddle-point problem, with particular applications in the area of total variation image restoration. This paper focuses on the convergence analysis of these primal-dual algorithms and shows that their involved parameters (including step sizes) can be significantly enlarged if some simple correction steps are supplemented. Some new primal-dual-based methods are thus proposed for solving the saddle-point problem. We show that these new methods are of the contraction type: the iterative sequences generated by these new methods are contractive with respect to the solution set of the saddle-point problem. The global convergence of these new methods thus can be obtained within the analytic framework of contraction-type methods. The novel study on these primal-dual algorithms from the perspective of contraction methods substantially simplifies existing convergence analysis. Finally, we show the efficiency of the new methods numerically. © 2012 Society for Industrial and Applied Mathematics.
Persistent Identifierhttp://hdl.handle.net/10722/250983
ISSN
2020 Impact Factor: 2.867
2020 SCImago Journal Rankings: 0.944
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorHe, Bingsheng-
dc.contributor.authorYuan, Xiaoming-
dc.date.accessioned2018-02-01T01:54:15Z-
dc.date.available2018-02-01T01:54:15Z-
dc.date.issued2012-
dc.identifier.citationSIAM Journal on Imaging Sciences, 2012, v. 5, n. 1, p. 119-149-
dc.identifier.issn1936-4954-
dc.identifier.urihttp://hdl.handle.net/10722/250983-
dc.description.abstractRecently, some primal-dual algorithms have been proposed for solving a saddle-point problem, with particular applications in the area of total variation image restoration. This paper focuses on the convergence analysis of these primal-dual algorithms and shows that their involved parameters (including step sizes) can be significantly enlarged if some simple correction steps are supplemented. Some new primal-dual-based methods are thus proposed for solving the saddle-point problem. We show that these new methods are of the contraction type: the iterative sequences generated by these new methods are contractive with respect to the solution set of the saddle-point problem. The global convergence of these new methods thus can be obtained within the analytic framework of contraction-type methods. The novel study on these primal-dual algorithms from the perspective of contraction methods substantially simplifies existing convergence analysis. Finally, we show the efficiency of the new methods numerically. © 2012 Society for Industrial and Applied Mathematics.-
dc.languageeng-
dc.publisherSociety for Industrial and Applied Mathematics. The Journal's web site is located at http://www.siam.org/journals/siims.php-
dc.relation.ispartofSIAM Journal on Imaging Sciences-
dc.subjectTotal variation-
dc.subjectProximal point algorithm-
dc.subjectPrimal-dual method-
dc.subjectImage restoration-
dc.subjectContraction method-
dc.subjectSaddle point problem-
dc.titleConvergence analysis of primal-dual algorithms for a saddle-point problem: From contraction perspective-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1137/100814494-
dc.identifier.scopuseid_2-s2.0-84856726346-
dc.identifier.volume5-
dc.identifier.issue1-
dc.identifier.spage119-
dc.identifier.epage149-
dc.identifier.isiWOS:000302220800005-
dc.identifier.issnl1936-4954-

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