Optimal and better transport plans
| dc.creator | Beiglböck, Mathias | |
| dc.creator | Goldstern, Martin | |
| dc.creator | Maresch, Gabriel | |
| dc.creator | Schachermayer, Walter | |
| dc.date | 2008-02-05 | |
| dc.date | 2009-01-19 | |
| dc.date.accessioned | 2026-07-07T12:30:51Z | |
| dc.date.available | 2026-07-07T12:30:51Z | |
| dc.description | We 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.description | 25 pages | |
| dc.identifier | https://arxiv.org/abs/0802.0646 | |
| dc.identifier | http://arxiv.org/abs/0802.0646 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/216264 | |
| dc.subject | Optimization and Control | |
| dc.subject | 49K27 (Primary); 28A05 (Secondary) | |
| dc.title | Optimal and better transport plans | |
| dc.type | text |