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Article: Customized proximal point algorithms for linearly constrained convex minimization and saddle-point problems: A unified approach

TitleCustomized proximal point algorithms for linearly constrained convex minimization and saddle-point problems: A unified approach
Authors
KeywordsSaddle-point problem
Proximal point algorithm
Customized algorithms
Convex minimization
Splitting algorithms
Convergence rate
Issue Date2014
Citation
Computational Optimization and Applications, 2014, v. 59, n. 1-2, p. 135-161 How to Cite?
AbstractThis paper focuses on some customized applications of the proximal point algorithm (PPA) to two classes of problems: the convex minimization problem with linear constraints and a generic or separable objective function, and a saddle-point problem. We treat these two classes of problems uniformly by a mixed variational inequality, and show how the application of PPA with customized metric proximal parameters can yield favorable algorithms which are able to make use of the models' structures effectively. Our customized PPA revisit turns out to unify some algorithms including some existing ones in the literature and some new ones to be proposed. From the PPA perspective, we establish the global convergence and a worst-case O(1/t) convergence rate for this series of algorithms in a unified way. © 2013 Springer Science+Business Media New York.
Persistent Identifierhttp://hdl.handle.net/10722/251269
ISSN
2020 Impact Factor: 2.167
2020 SCImago Journal Rankings: 1.028
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorGu, Guoyong-
dc.contributor.authorHe, Bingsheng-
dc.contributor.authorYuan, Xiaoming-
dc.date.accessioned2018-02-01T01:55:04Z-
dc.date.available2018-02-01T01:55:04Z-
dc.date.issued2014-
dc.identifier.citationComputational Optimization and Applications, 2014, v. 59, n. 1-2, p. 135-161-
dc.identifier.issn0926-6003-
dc.identifier.urihttp://hdl.handle.net/10722/251269-
dc.description.abstractThis paper focuses on some customized applications of the proximal point algorithm (PPA) to two classes of problems: the convex minimization problem with linear constraints and a generic or separable objective function, and a saddle-point problem. We treat these two classes of problems uniformly by a mixed variational inequality, and show how the application of PPA with customized metric proximal parameters can yield favorable algorithms which are able to make use of the models' structures effectively. Our customized PPA revisit turns out to unify some algorithms including some existing ones in the literature and some new ones to be proposed. From the PPA perspective, we establish the global convergence and a worst-case O(1/t) convergence rate for this series of algorithms in a unified way. © 2013 Springer Science+Business Media New York.-
dc.languageeng-
dc.relation.ispartofComputational Optimization and Applications-
dc.subjectSaddle-point problem-
dc.subjectProximal point algorithm-
dc.subjectCustomized algorithms-
dc.subjectConvex minimization-
dc.subjectSplitting algorithms-
dc.subjectConvergence rate-
dc.titleCustomized proximal point algorithms for linearly constrained convex minimization and saddle-point problems: A unified approach-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1007/s10589-013-9616-x-
dc.identifier.scopuseid_2-s2.0-84906949008-
dc.identifier.volume59-
dc.identifier.issue1-2-
dc.identifier.spage135-
dc.identifier.epage161-
dc.identifier.eissn1573-2894-
dc.identifier.isiWOS:000341495800008-
dc.identifier.issnl0926-6003-

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