Characterization of optimal Transport Plans for the Monge-Kantorovich-Problem

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We prove that $c$-cyclically monotone transport plans $π$ optimize the Monge-Kantorovich transportation problem under an additional measurability condition. This measurability condition is always satisfied for finitely valued, lower semi-continuous cost functions. In particular, this yields a positive answer to Problem 2.25 in C. Villani's book. We emphasize that we do not need any regularity conditions as were imposed in the previous literature.
to appear in Proceedings of the AMS

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Optimization and Control, Functional Analysis, 49J45,28A35

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http://salesiana.dossiersoluciones.com/handle/123456789/141717

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0711.1268
 http://arxiv.org/abs/0711.1268

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arXiv