Afficher la notice abrégée

dc.contributor.authorLiang, Jingwei
dc.contributor.authorFadili, Jalal M.
dc.contributor.authorPeyré, Gabriel
dc.date.accessioned2019-01-11T14:49:56Z
dc.date.available2019-01-11T14:49:56Z
dc.date.issued2018
dc.identifier.issn0233-1934
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/18370
dc.language.isoenen
dc.subjectLocal Linear Convergenceen
dc.subjectDouglas-Rachford/ADMM Partial Smoothnessen
dc.subjectForward-Backward splittingen
dc.subjectPrimal-Dual splittingen
dc.subject.ddc621.3en
dc.titleLocal Linear Convergence Analysis of Primal-Dual Splitting Methodsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIn this paper, we study the local linear convergence properties of a versatile class of Primal-Dual splitting methods for minimizing composite non-smooth convex optimization problems. Under the assumption that the non-smooth components of the problem are partly smooth relative to smooth manifolds, we present a unified local convergence analysis framework for these methods. More precisely, in our framework we first show that (i) the sequences generated by Primal-Dual splitting methods identify a pair of primal and dual smooth manifolds in a finite number of iterations, and then (ii) enter a local linear convergence regime, which is characterized based on the structure of the underlying active smooth manifolds. We also show how our results for Primal-Dual splitting can be specialized to cover existing ones on Forward-Backward splitting and Douglas-Rachford splitting/ADMM (al-ternating direction methods of multipliers). Moreover, based on these obtained local convergence analysis result, several practical acceleration techniques are discussed. To exemplify the usefulness of the obtained result, we consider several concrete numerical experiments arising from fields including signal/image processing, inverse problems and machine learning, etc. The demonstration not only verifies the local linear convergence behaviour of Primal-Dual splitting methods, but also the insights on how to accelerate them in practice.en
dc.relation.isversionofjnlnameOptimization. A Journal of Mathematical Programming and Operations Research
dc.relation.isversionofjnlvol67en
dc.relation.isversionofjnlissue6en
dc.relation.isversionofjnldate2018-01
dc.relation.isversionofjnlpages821-853en
dc.relation.isversionofdoi10.1080/02331934.2018.1426584en
dc.relation.isversionofjnlpublisherTaylor & Francisen
dc.subject.ddclabelTraitement du signalen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2019-01-11T14:46:08Z
hal.person.labIds150
hal.person.labIds150
hal.person.labIds60


Fichiers attachés à cette notice

Thumbnail

Ce document fait partie de la (des) collection(s) suivante(s)

Afficher la notice abrégée