Duality for Borel measurable cost functions

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We consider the Monge-Kantorovich transport problem in an abstract measure theoretic setting. Our main result states that duality holds if $c:X\times Y\to [0,\infty)$ is an arbitrary Borel measurable cost function on the product of Polish spaces $X,Y$. In the course of the proof we show how to relate a non - optimal transport plan to the optimal transport costs via a ``subsidy'' function and how to identify the dual optimizer. We also provide some examples showing the limitations of the duality relations.

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Optimization and Control, 49K27; 28A05

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http://salesiana.dossiersoluciones.com/handle/123456789/164569

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0807.1468
 http://arxiv.org/abs/0807.1468

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arXiv