A differential approach to the multi-marginal Schrödinger system

Guillaume Carlier (1, 2) , Maxime Laborde (3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales
3 Department of Mathematics and Statistics [Montréal]

We develop an elementary and self-contained differential approach, in an L ∞ setting, for well-posedness (existence, uniqueness and smooth dependence with respect to the data) for the multi-marginal Schrödinger system which arises in the entropic regularization of optimal transport problems.

Mots clés: Local and global inverse function theorems; Entropy minimization; Multi-marginal Schrödinger system

Domaines: Analyse fonctionnelle [math.FA]; Optimisation et contrôle [math.OC]

Guillaume Carlier, Maxime Laborde. A differential approach to the multi-marginal Schrödinger system. SIAM Journal on Mathematical Analysis, 2020, ⟨10.1137/19M1253800⟩. ⟨hal-01918578v2⟩