A saddle-point approach to the Monge-Kantorovich optimal transport problem

Christian Léonard (1)

1 MODAL'X - Modélisation aléatoire de Paris X

The Monge-Kantorovich problem is revisited by means of a variant of the saddle-point method without appealing to cyclical $c$-monotonicity and $c$-conjugates. One gives new proofs of the well-known Kantorovich dual equality and a sufficient optimality condition which has recently been proved by W. Schachermayer and J. Teichman. A new necessary optimality condition is obtained in the case where the cost function takes infinite values.

Mots clés: convex optimization; saddle-point; conjugate duality; optimal transport

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

Christian Léonard. A saddle-point approach to the Monge-Kantorovich optimal transport problem. ESAIM: Control, Optimisation and Calculus of Variations, 2010, published online. ⟨10.1051/cocv/2010013⟩. ⟨hal-00177362⟩