We study the entropic regularization of the optimal transport problem in dimension 1 when the cost function is the distance c(x, y) = |y − x|. The selected plan at the limit is, among those which are optimal for the non-penalized problem, the most " diffuse " one on the zones where it may have a density.
Publié le : 2018-07-03
Classification:
Entropic regularization,
Monotone rearrangement,
Monge problem,
Optimal transportation,
Gamma-convergence,
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
@article{hal-01498732,
author = {Di Marino, Simone and Louet, Jean},
title = {The entropic regularization of the Monge problem on the real line},
journal = {HAL},
volume = {2018},
number = {0},
year = {2018},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-01498732}
}
Di Marino, Simone; Louet, Jean. The entropic regularization of the Monge problem on the real line. HAL, Tome 2018 (2018) no. 0, . http://gdmltest.u-ga.fr/item/hal-01498732/