Characterization of optimal Transport Plans for the Monge-Kantorovich-Problem
Optimization and Control
2007-11-09 v1 Functional Analysis
Abstract
We prove that -cyclically monotone transport plans 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.
Keywords
Cite
@article{arxiv.0711.1268,
title = {Characterization of optimal Transport Plans for the Monge-Kantorovich-Problem},
author = {Walter Schachermayer and Josef Teichmann},
journal= {arXiv preprint arXiv:0711.1268},
year = {2007}
}
Comments
to appear in Proceedings of the AMS