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Uniquely minimizing costs for the Kantorovitch problem
Abbas Moameni1 ; Ludovic Rifford2
1 School of Mathematics and Statistics, Carleton University, Ottawa, Ontario (Canada)
2 Université Côte d’Azur, CNRS, Inria, Labo. J.-A. Dieudonné, UMR CNRS 7351, Parc Valrose, 06108 Nice Cedex 02 (France)
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 3, pp. 507-563.

L’objet de cet article est de mettre en évidence des conditions suffisantes pertinentes et efficaces qui garantissent l’unicité des solutions aux problème de Kantorovitch et de démontrer la densité des coûts continus sur une variété pour lesquels les plans de transport optimaux sont uniques. Nous proposons également un critère pratique pour l’unicité des solutions au problème de Kantorovitch dans le cadre d’espaces polonais non-compacts.

The purpose of the present paper is to establish comprehensive and systematic sufficient conditions for uniqueness of the Kantorovitch optimizer, and to prove the density of continuous costs on arbitrary manifolds for which optimal plans are unique. We shall also establish a practical criterion for the uniqueness of the Kantorovitch optimizer in the non-compact setting on Polish spaces.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/afst.1638
Abbas Moameni 1 ; Ludovic Rifford 2

1 School of Mathematics and Statistics, Carleton University, Ottawa, Ontario (Canada)
2 Université Côte d’Azur, CNRS, Inria, Labo. J.-A. Dieudonné, UMR CNRS 7351, Parc Valrose, 06108 Nice Cedex 02 (France)
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Uniquely minimizing costs for the {Kantorovitch} problem},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
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Abbas Moameni; Ludovic Rifford. Uniquely minimizing costs for the Kantorovitch problem. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 3, pp. 507-563. doi : 10.5802/afst.1638. https://afst.centre-mersenne.org/articles/10.5802/afst.1638/

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