A general duality theorem for the Monge-Kantorovich transport problem

• Autorzy: Mathias Beiglböck , Christian Léonard , Walter Schachermayer
• Języki publikacji: EN

Abstrakty

EN

The duality theory for 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. Our main result states that in this setting there is no duality gap provided the optimal transport problem is formulated in a suitably relaxed way. The relaxed transport problem is defined as the limiting cost of the partial transport of masses 1 - ε from (X,μ) to (Y,ν) as ε > 0 tends to zero.
The classical duality theorems of H. Kellerer, where c is lower semicontinuous or uniformly bounded, quickly follow from these general results.

Kategorie tematyczne

• 49Q20: Variational problems in a geometric measure-theoretic setting

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 209
• Numer: 2
• Strony: 151-167

Daty

wydano

2012

Twórcy

autor

Mathias Beiglböck

• Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, 1090 Wien, Austria

autor

Christian Léonard

• Modal-X, Université Paris Ouest, Bât. G, 200 av. de la République, 92001 Nanterre, France

autor

Walter Schachermayer

• Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, 1090 Wien, Austria

Identyfikatory

DOI

10.4064/sm209-2-4