Geodesic
A generalized dual maximizer for the Monge-Kantorovich transport problem
ESAIM: Probability and Statistics, Tome 16 (2012), pp. 306-323 Cet article a éte moissonné depuis la source Numdam

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The dual attainment of the Monge-Kantorovich transport problem is analyzed in a general setting. The spaces X,Y are assumed to be polish and equipped with Borel probability measures μ and ν. The transport cost function c : X × Y →  [0,∞]  is assumed to be Borel measurable. We show that a dual optimizer always exists, provided we interpret it as a projective limit of certain finitely additive measures. Our methods are functional analytic and rely on Fenchel's perturbation technique.

DOI : 10.1051/ps/2011163
Classification : 46E30, 46N10, 49J45, 28A35
Keywords: optimal transport, duality in function spaces, Fenchel's perturbation technique 
@article{PS_2012__16__306_0,
     author = {Beiglb\"ock, Mathias and L\'eonard, Christian and Schachermayer, Walter},
     title = {A generalized dual maximizer for the {Monge-Kantorovich} transport problem},
     journal = {ESAIM: Probability and Statistics},
     pages = {306--323},
     year = {2012},
     publisher = {EDP-Sciences},
     volume = {16},
     doi = {10.1051/ps/2011163},
     mrnumber = {2956577},
     zbl = {1263.49057},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2011163/}
}
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Beiglböck, Mathias; Léonard, Christian; Schachermayer, Walter. A generalized dual maximizer for the Monge-Kantorovich transport problem. ESAIM: Probability and Statistics, Tome 16 (2012), pp. 306-323. doi: 10.1051/ps/2011163

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