Wasserstein interpolation with constraints and application to a parking problem
Buttazzo, Giuseppe; Carlier, Guillaume; Eichinger, Katharina (2022), Wasserstein interpolation with constraints and application to a parking problem. https://basepub.dauphine.psl.eu/handle/123456789/23682
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Type
Document de travail / Working paperDate
2022Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSLPublished in
Paris
Pages
30
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Show full item recordAuthor(s)
Buttazzo, GiuseppeDipartimento di Matematica [Pisa]
Carlier, Guillaume
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Eichinger, Katharina
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We consider optimal transport problems where the cost for transporting a given probability measure μ0 to another one μ1 consists of two parts: the first one measures the transportation from μ0 to an intermediate (pivot) measure μ to be determined (and subject to various constraints), and the second one measures the transportation from μ to μ1. This leads to Wasserstein interpolation problems under constraints for which we establish various properties of the optimal pivot measures μ. Considering the more general situation where only some part of the mass uses the intermediate stop leads to a mathematical model for the optimal location of a parking region around a city. Numerical simulations, based on entropic regularization, are presented both for the optimal parking regions and for Wasserstein constrained interpolation problems.Subjects / Keywords
optimal transport; Wasserstein distance; measure interpolation; optimal parking regionsRelated items
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