Optimal and better transport plans |
| |
Authors: | Mathias Beiglböck Martin Goldstern Walter Schachermayer |
| |
Institution: | a Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstraße 8-10/104, 1040 Wien, Austria b Fakultät für Mathematik, Universität Wien, Nordbergstraße 15, 1090 Wien, Austria |
| |
Abstract: | 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 ∞. We show that this is true in a more general setting, in particular for merely Borel measurable cost functions provided that {c=∞} 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. |
| |
Keywords: | Monge-Kantorovich problem c-Cyclically monotone Strongly c-monotone Measurable cost function |
本文献已被 ScienceDirect 等数据库收录! |
|