The entropic regularization of the Monge problem on the real line

Simone Di Marino (1) , Jean Louet (2, 3)

1 SNS - Scuola Normale Superiore di Pisa
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales

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.

Mots clés: Monotone rearrangement; Monge problem; Optimal transportation; Gamma-convergence; Entropic regularization

Domaines: Optimisation et contrôle [math.OC]

Simone Di Marino, Jean Louet. The entropic regularization of the Monge problem on the real line. SIAM Journal on Mathematical Analysis, In press, 50 (4), pp.3451 - 3477. ⟨10.1137/17M1123523⟩. ⟨hal-01498732v4⟩