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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

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Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-01261094
Date
2018
Journal name
ESAIM: Mathematical Modelling and Numerical Analysis
Volume
52
Number
6 (November-December 2018 )
Pages
2133 - 2148
Publication identifier
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Author(s)
Benamou, Jean-David
INRIA 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 Lagrangian