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On the convergence of augmented Lagrangian method for optimal transport between nonnegative densities

hal.structure.identifierEquations aux Dérivées Partielles [EDP]
hal.structure.identifierJohann Radon Institute for Computational and Applied Mathematics [RICAM]
dc.contributor.authorHUG, Romain
hal.structure.identifierEquations aux Dérivées Partielles [EDP]
dc.contributor.authorMAITRE, Emmanuel
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorPAPADAKIS, Nicolas
dc.date.accessioned2024-04-04T02:59:54Z
dc.date.available2024-04-04T02:59:54Z
dc.date.issued2020-05-15
dc.identifier.issn0022-247X
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192780
dc.description.abstractEnThe dynamical formulation of the optimal transport problem, introduced by J. D. Benamou and Y. Brenier, corresponds to the time-space search of a density and a momentum minimizing a transport energy between two densities. In order to solve this problem, an algorithm has been proposed to estimate a saddle point of a Lagrangian. We will study the convergence of this algorithm to a saddle point of the Lagrangian, in the most general conditions, particularly in cases where initial and final densities vanish on some areas of the transportation domain. The principal difficulty of our study will consist in the proof, under these conditions, of the existence of a saddle point, and especially in the uniqueness of the density-momentum component. Indeed, these conditions imply to have to deal with non-regular optimal transportation maps. For these reasons, a detailed study of the properties of the velocity field associated to an optimal transportation map in quadratic space is required.
dc.description.sponsorshipGeneralized Optimal Transport Models for Image processing - ANR-16-CE33-0010
dc.language.isoen
dc.publisherElsevier
dc.title.enOn the convergence of augmented Lagrangian method for optimal transport between nonnegative densities
dc.typeArticle de revue
dc.identifier.doi10.1016/j.jmaa.2019.123811
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.subject.halSciences de l'ingénieur [physics]/Traitement du signal et de l'image
bordeaux.journalJournal of Mathematical Analysis and Applications
bordeaux.page123811
bordeaux.volume485
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue2
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01128793
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01128793v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Mathematical%20Analysis%20and%20Applications&rft.date=2020-05-15&rft.volume=485&rft.issue=2&rft.spage=123811&rft.epage=123811&rft.eissn=0022-247X&rft.issn=0022-247X&rft.au=HUG,%20Romain&MAITRE,%20Emmanuel&PAPADAKIS,%20Nicolas&rft.genre=article


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