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A saddle-point approach to the Monge-Kantorovichoptimal 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 variantof the saddle-point method without appealing to c-conjugates. Anew abstract characterization of the optimal plans is obtained inthe case where the cost function takes infinite values. It leadsus to new explicit sufficient and necessary optimality conditions.As by-products, we obtain a new proof of the well-knownKantorovich dual equality and an improvement of the convergence ofthe 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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