Minimal convex extensions and finite difference discretization of the quadratic Monge-Kantorovich problem

Jean-David Benamou 1 Vincent Duval 1
1 MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales
CEREMADE - CEntre de REcherches en MAthématiques de la DEcision, Inria de Paris
Abstract : We present an adaptation of the MA-LBR scheme to the Monge-Ampère equation with second boundary value condition, provided the target is a convex set. This yields a fast adaptive method to numerically solve the Optimal Transport problem between two absolutely continuous measures, the second of which has convex support. The proposed numerical method actually captures a specific Brenier solution which is minimal in some sense. We prove the convergence of the method as the grid stepsize vanishes and we show with numerical experiments that it is able to reproduce subtle properties of the Optimal Transport problem.
Type de document :
Pré-publication, Document de travail
2017
Liste complète des métadonnées

https://hal.inria.fr/hal-01616842
Contributeur : Vincent Duval <>
Soumis le : mardi 31 octobre 2017 - 09:47:45
Dernière modification le : jeudi 11 janvier 2018 - 06:28:03

Fichiers

MABV2final.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01616842, version 2
  • ARXIV : 1710.05594

Collections

Citation

Jean-David Benamou, Vincent Duval. Minimal convex extensions and finite difference discretization of the quadratic Monge-Kantorovich problem. 2017. 〈hal-01616842v2〉

Partager

Métriques

Consultations de la notice

115

Téléchargements de fichiers

21