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dc.contributor.authorBenamou, Jean-David
dc.contributor.authorFroese, Brittany D.
dc.date.accessioned2019-04-23T09:12:18Z
dc.date.available2019-04-23T09:12:18Z
dc.date.issued2014
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/18736
dc.language.isoenen
dc.subjectoptimal transportationen
dc.subjectMonge-Ampere equationen
dc.subjectAleksandrov solutionsen
dc.subjectviscosity solutionsen
dc.subjectfinite difference methodsen
dc.subject.ddc515en
dc.titleA viscosity framework for computing Pogorelov solutions of the Monge-Ampere equationen
dc.typeDocument de travail / Working paper
dc.description.abstractenWe consider the Monge-Kantorovich optimal transportation problem between two measures, one of which is a weighted sum of Diracs. This problem is traditionally solved using expensive geometric methods. It can also be reformulated as an elliptic partial differential equation known as the Monge-Ampere equation. However, existing numerical methods for this non-linear PDE require the measures to have finite density. We introduce a new formulation that couples the viscosity and Aleksandrov solution definitions and show that it is equivalent to the original problem. Moreover, we describe a local reformulation of the subgradient measure at the Diracs, which makes use of one-sided directional derivatives. This leads to a consistent, monotone discretisation of the equation. Computational results demonstrate the correctness of this scheme when methods designed for conventional viscosity solutions fail.en
dc.publisher.nameCahier de recherche CEREMADE, Université Paris-Dauphineen
dc.publisher.cityParisen
dc.identifier.citationpages24en
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris-Dauphineen
dc.subject.ddclabelAnalyseen
dc.identifier.citationdate2014
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2019-03-27T11:02:45Z
hal.person.labIds60
hal.person.labIds118885


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