A saddle-point approach to the Monge-Kantorovich optimal transport problem
Modal-X, Université Paris Ouest, Bât. G, 200 av. de la République, 92001 Nanterre, France. firstname.lastname@example.org
The Monge-Kantorovich problem is revisited by means of a variant of the saddle-point method without appealing to c-conjugates. A new abstract characterization of the optimal plans is obtained in the case where the cost function takes infinite values. It leads us to new explicit sufficient and necessary optimality conditions. As by-products, we obtain a new proof of the well-known Kantorovich dual equality and an improvement of the convergence of the minimizing sequences.
Mathematics Subject Classification: 46N10 / 49J45 / 28A35
Key words: Convex optimization / saddle-point / conjugate duality / optimal transport
© EDP Sciences, SMAI, 2010