| Issue |
ESAIM: M2AN
Volume 52, Number 5, September–October 2018
|
|
|---|---|---|
| Page(s) | 2109 - 2132 | |
| DOI | https://doi.org/10.1051/m2an/2018001 | |
| Published online | 25 January 2019 | |
Optimal partial transport problem with Lagrangian costs
1
Institut de recherche XLIM-DMI, UMR-CNRS 6172, Faculté des Sciences et Techniques, Université de Limoges, France .
2
Department of Mathematics, Quy Nhon University, Vietnam .
* Corresponding author: noureddine.igbida@unilim.fr
Received:
16
June
2017
Accepted:
7
January
2018
We introduce a dual dynamical formulation for the optimal partial transport problem with Lagrangian costs
based on a constrained Hamilton–Jacobi equation. Optimality condition is given that takes the form of a system of PDEs in some way similar to constrained mean field games. The equivalent formulations are then used to give numerical approximations to the optimal partial transport problem via augmented Lagrangian methods. One of advantages is that the approach requires only values of L and does not need to evaluate cL(x, y), for each pair of endpoints x and y, which comes from a variational problem. This method also provides at the same time active submeasures and the associated optimal transportation.
Key words: Optimal transport / optimal partial transport / Fenchel–Rockafellar duality / augmented Lagrangian method
© The authors. Published by EDP Sciences, SMAI 2019
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