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

Published online by Cambridge University Press:  31 March 2010

Christian Léonard
Christian Léonard*
Affiliation:
Modal-X, Université Paris Ouest, Bât. G, 200 av. de la République, 92001 Nanterre, France. christian.leonard@u-paris10.fr
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Abstract

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.

Keywords

Convex optimizationsaddle-pointconjugate dualityoptimal transport
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 17 , Issue 3 , July 2011 , pp. 682 - 704
Copyright
© EDP Sciences, SMAI, 2010

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