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.
Mots clés : 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},
publisher = {EDP-Sciences},
volume = {16},
year = {2012},
doi = {10.1051/ps/2011163},
mrnumber = {2956577},
zbl = {1263.49057},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps/2011163/}
}
TY - JOUR AU - Beiglböck, Mathias AU - Léonard, Christian AU - Schachermayer, Walter TI - A generalized dual maximizer for the Monge-Kantorovich transport problem JO - ESAIM: Probability and Statistics PY - 2012 SP - 306 EP - 323 VL - 16 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2011163/ DO - 10.1051/ps/2011163 LA - en ID - PS_2012__16__306_0 ER -
%0 Journal Article %A Beiglböck, Mathias %A Léonard, Christian %A Schachermayer, Walter %T A generalized dual maximizer for the Monge-Kantorovich transport problem %J ESAIM: Probability and Statistics %D 2012 %P 306-323 %V 16 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps/2011163/ %R 10.1051/ps/2011163 %G en %F PS_2012__16__306_0
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. http://archive.numdam.org/articles/10.1051/ps/2011163/
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