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The Proximal Alternating Minimization Algorithm for Two-Block Separable Convex Optimization Problems with Linear Constraints

dc.contributor.authorBitterlich, Sandy
dc.contributor.authorBoţ, Radu Ioan
dc.contributor.authorCsetnek, Ernö Robert
dc.contributor.authorWanka, Gert
dc.date.accessioned2019-03-28T14:32:13Z
dc.date.available2019-03-28T14:32:13Z
dc.date.issued2018de
dc.relation.ISSN1573-2878de
dc.identifier.urihttp://resolver.sub.uni-goettingen.de/purl?gs-1/15982
dc.description.abstractThe Alternating Minimization Algorithm has been proposed by Paul Tseng to solve convex programming problems with two-block separable linear constraints and objectives, whereby (at least) one of the components of the latter is assumed to be strongly convex. The fact that one of the subproblems to be solved within the iteration process of this method does not usually correspond to the calculation of a proximal operator through a closed formula affects the implementability of the algorithm. In this paper, we allow in each block of the objective a further smooth convex function and propose a proximal version of the algorithm, which is achieved by equipping the algorithm with proximal terms induced by variable metrics. For suitable choices of the latter, the solving of the two subproblems in the iterative scheme can be reduced to the computation of proximal operators. We investigate the convergence of the proposed algorithm in a real Hilbert space setting and illustrate its numerical performances on two applications in image processing and machine learning.de
dc.language.isoengde
dc.rightsopenAccess
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectProximal AMA; Lagrangian; Saddle points; Subdifferential; Convex optimization; Fenchel dualityde
dc.subject.ddc510
dc.titleThe Proximal Alternating Minimization Algorithm for Two-Block Separable Convex Optimization Problems with Linear Constraintsde
dc.typejournalArticlede
dc.identifier.doi10.1007/s10957-018-01454-y
dc.type.versionpublishedVersionde
dc.relation.pISSN0022-3239
dc.relation.eISSN1573-2878
dc.type.subtypejournalArticle
dc.description.statuspeerReviewedde
dc.bibliographicCitation.journalJournal of Optimization Theory and Applicationsde


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