
A numerical solution to Monge's problem with a Finsler distance as cost
Benamou, Jean-David; Carlier, Guillaume; Hatchi, Roméo (2018), A numerical solution to Monge's problem with a Finsler distance as cost, ESAIM: Mathematical Modelling and Numerical Analysis, 52, 6 (November-December 2018 ), p. 2133 - 2148. 10.1051/m2an/2016077
View/ Open
Type
Article accepté pour publication ou publiéExternal document link
https://hal.archives-ouvertes.fr/hal-01261094Date
2018Journal name
ESAIM: Mathematical Modelling and Numerical AnalysisVolume
52Number
6 (November-December 2018 )Pages
2133 - 2148
Publication identifier
Metadata
Show full item recordAuthor(s)
Benamou, Jean-DavidINRIA Rocquencourt
Carlier, Guillaume
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Hatchi, Roméo
Abstract (EN)
Monge's problem with a Finsler cost is intimately related to an optimal flow problem. Discretization of this problem and its dual leads to a well-posed finite-dimensional saddle-point problem which can be solved numerically relatively easily by an augmented Lagrangian approach in the same spirit as the Benamou-Brenier method for the optimal transport problem with quadratic cost. Numerical results validate the method. We also emphasize that the algorithm only requires elementary operations and in particular never involves evaluation of the Finsler distance or of geodesics.Subjects / Keywords
Monge's problem; Finsler distance; augmented LagrangianRelated items
Showing items related by title and author.
-
Benamou, Jean-David; Carlier, Guillaume; Nenna, Luca (2017) Chapitre d'ouvrage
-
Benamou, Jean-David; Carlier, Guillaume; Bonne, Nicolas (2013) Rapport
-
Benamou, Jean-David; Carlier, Guillaume; Mérigot, Quentin; Oudet, Edouard (2016) Article accepté pour publication ou publié
-
Benamou, Jean-David; Carlier, Guillaume; Cuturi, Marco; Nenna, Luca; Peyré, Gabriel (2015) Article accepté pour publication ou publié
-
Benamou, Jean-David; Carlier, Guillaume; Laborde, Maxime (2016) Article accepté pour publication ou publié