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

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

2007-11-08

arxiv.org/abs/0711.1268v1

Mathematics

Optimization and Control

to appear in Proceedings of the AMS

Scientific paper

We prove that $c$-cyclically monotone transport plans $\pi$ 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.

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