Show simple item record

hal.structure.identifierDépartement de Mathématiques et Applications - ENS Paris [DMA]
hal.structure.identifierLaboratoire de Probabilités, Statistiques et Modélisations [LPSM (UMR_8001)]
dc.contributor.authorBoyer, Claire
HAL ID: 175633
*
hal.structure.identifierCentre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
dc.contributor.authorChambolle, Antonin
HAL ID: 184536
ORCID: 0000-0002-9465-4659
*
hal.structure.identifierLaboratoire de Mathématiques d'Orsay [LMO]
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorDe Castro, Yohann
HAL ID: 3151
*
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorDuval, Vincent
HAL ID: 7243
ORCID: 0000-0002-7709-256X
*
hal.structure.identifierInstitut de Mathématiques de Toulouse UMR5219 [IMT]
dc.contributor.authorde Gournay, Frédéric
HAL ID: 7855
ORCID: 0000-0003-4721-3137
*
hal.structure.identifier
dc.contributor.authorWeiss, Pierre
HAL ID: 175985
ORCID: 0000-0002-4785-9133
*
dc.date.accessioned2019-09-24T12:22:19Z
dc.date.available2019-09-24T12:22:19Z
dc.date.issued2019
dc.identifier.issn1052-6234
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/19905
dc.language.isoenen
dc.subjectTotal variation
dc.subjectVector space
dc.subjectConvex regularization
dc.subjectRepresenter theorem
dc.subjectInverse problems
dc.subject.ddc515en
dc.titleOn Representer Theorems and Convex Regularization
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe establish a general principle which states that regularizing an inverse problem with a convex function yields solutions that are convex combinations of a small number of atoms. These atoms are identified with the extreme points and elements of the extreme rays of the regularizer level sets. An extension to a broader class of quasi-convex regularizers is also discussed. As a side result, we characterize the minimizers of the total gradient variation, which was previously an unresolved problem.
dc.relation.isversionofjnlnameSIAM Journal on Optimization
dc.relation.isversionofjnlvol29
dc.relation.isversionofjnlissue2
dc.relation.isversionofjnldate2019
dc.relation.isversionofjnlpages1260–1281
dc.relation.isversionofdoi10.1137/18M1200750
dc.relation.isversionofjnlpublisherSIAM - Society for Industrial and Applied Mathematics
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2020-12-09T14:37:08Z
hal.author.functionaut
hal.author.functionaut
hal.author.functionaut
hal.author.functionaut
hal.author.functionaut
hal.author.functionaut


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record