A Numerical Method to solve Optimal Transport Problems with Coulomb Cost

Abstract : In this paper, we present a numerical method, based on iterative Bregman projections, to solve the optimal transport problem with Coulomb cost. This is related to the strong interaction limit of Density Functional Theory. The first idea is to introduce an entropic regularization of the Kantorovich formulation of the Optimal Transport problem. The regularized problem then corresponds to the projection of a vector on the intersection of the constraints with respect to the Kullback-Leibler distance. Iterative Bregman projections on each marginal constraint are explicit which enables us to approximate the optimal transport plan. We validate the numerical method against analytical test cases.
Type de document :
Pré-publication, Document de travail
2015
Liste complète des métadonnées

Littérature citée [34 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-01148954
Contributeur : Jean-David Benamou <>
Soumis le : vendredi 8 mai 2015 - 07:14:50
Dernière modification le : jeudi 11 janvier 2018 - 06:12:21
Document(s) archivé(s) le : mercredi 19 avril 2017 - 19:58:00

Fichier

chapter_DFT_Benamou_Carlier_Ne...
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01148954, version 2

Collections

Citation

Jean-David Benamou, Guillaume Carlier, Luca Nenna. A Numerical Method to solve Optimal Transport Problems with Coulomb Cost. 2015. 〈hal-01148954v2〉

Partager

Métriques

Consultations de la notice

342

Téléchargements de fichiers

317