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
TypeArticle accepté pour publication ou publié
External document linkhttps://hal.archives-ouvertes.fr/hal-01261094
Journal nameESAIM: Mathematical Modelling and Numerical Analysis
Number6 (November-December 2018 )
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
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 / KeywordsMonge's problem; Finsler distance; augmented Lagrangian
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Benamou, Jean-David; Carlier, Guillaume; Cuturi, Marco; Nenna, Luca; Peyré, Gabriel (2015) Article accepté pour publication ou publié