Geodesic
A numerical solution to Monge’s problem with a Finsler distance as cost
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 6, pp. 2133-2148

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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.

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DOI : 10.1051/m2an/2016077
Classification : 65K10, 90C25, 90C46
Keywords: Monge’s problem, Finsler distance, augmented Lagrangian

Benamou, Jean-David 1 ; Carlier, Guillaume 1 ; Hatchi, Roméo 

1 
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Benamou, Jean-David; Carlier, Guillaume; Hatchi, Roméo. A numerical solution to Monge’s problem with a Finsler distance as cost. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 6, pp. 2133-2148. doi: 10.1051/m2an/2016077

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