Optimal and better transport plans

dc.creatorBeiglböck, Mathias
dc.creatorGoldstern, Martin
dc.creatorMaresch, Gabriel
dc.creatorSchachermayer, Walter
dc.date2008-02-05
dc.date2009-01-19
dc.date.accessioned2026-07-07T12:30:51Z
dc.date.available2026-07-07T12:30:51Z
dc.descriptionWe consider the Monge-Kantorovich transport problem in a purely measure theoretic setting, i.e. without imposing continuity assumptions on the cost function. It is known that transport plans which are concentrated on c-monotone sets are optimal, provided the cost function c is either lower semi-continuous and finite, or continuous and may possibly attain the value infty. We show that this is true in a more general setting, in particular for merely Borel measurable cost functions provided that {c=infty} is the union of a closed set and a negligible set. In a previous paper Schachermayer and Teichmann considered strongly c-monotone transport plans and proved that every strongly c-monotone transport plan is optimal. We establish that transport plans are strongly c-monotone if and only if they satisfy a "better" notion of optimality called robust optimality.
dc.description25 pages
dc.identifierhttps://arxiv.org/abs/0802.0646
dc.identifierhttp://arxiv.org/abs/0802.0646
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/216264
dc.subjectOptimization and Control
dc.subject49K27 (Primary); 28A05 (Secondary)
dc.titleOptimal and better transport plans
dc.typetext

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