| Issue |
ESAIM: M2AN
Volume 52, Number 6, November-December 2018
|
|
|---|---|---|
| Page(s) | 2133 - 2148 | |
| DOI | https://doi.org/10.1051/m2an/2016077 | |
| Published online | 01 February 2019 | |
Research Article
A numerical solution to Monge’s problem with a Finsler distance as cost
1
INRIA Rocquencourt, Domaine de Voluceau, 78153 Le Chesnay, France
2
CEREMADE, UMR CNRS 7534, Université Paris IX Dauphine, Pl. de Lattre de Tassigny, 75775 Paris Cedex 16, France
* Corresponding author: carlier@ceremade.dauphine.fr
Received:
23
January
2016
Accepted:
5
December
2016
Monge’s problem with a Finsler cost is intimately related to an optimal ow 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.
Mathematics Subject Classification: 65K10 / 90C25 / 90C46
Key words: Monge’s problem / Finsler distance / augmented Lagrangian
© EDP Sciences, SMAI 2019
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