Duality for Borel measurable cost functions

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dc.creatorBeiglböck, Mathias
dc.creatorSchachermayer, Walter
dc.date2008-07-09
dc.date.accessioned2026-07-07T09:49:23Z
dc.date.available2026-07-07T09:49:23Z
dc.descriptionWe 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.
dc.identifierhttps://arxiv.org/abs/0807.1468
dc.identifierhttp://arxiv.org/abs/0807.1468
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/164569
dc.subjectOptimization and Control
dc.subject49K27; 28A05
dc.titleDuality for Borel measurable cost functions
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