Duality for Borel measurable cost functions
By Mathias Beiglbock, Walter Schachermayer. 2008
51 citations recorded by the source corpus.
We consider the Monge-Kantorovich transport problem in an abstract measure theoretic setting. Our main result states that duality holds if c: X x Y → [0, ∞) 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.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/5e5b96fb5783177c1ce2d37f40a749c8145b3e1c
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In Applied Mathematics
- Julio D. Backhoff Veraguas
- Victor M. Panaretos
- Martin Huesmann
- Beatrice Acciaio
- Anastasiia Zalashko
- Mathias Beiglbock
- Alexander M. G. Cox
- Yoav Zemel
In Geometry and Topology
- Julio D. Backhoff Veraguas
- Beatrice Acciaio
- Anastasiia Zalashko
- Martin Huesmann
- Mathias Beiglbock
- Alexander M. G. Cox
- Victor M. Panaretos
- Yoav Zemel
Citations in the corpus
- Optimal transport and Skorokhod embedding (2013, background): “nvex analysis and the study of the relation to optimality we mention [Roc66, KS92, Ru¨s96, GM96]. Intuitively speaking, 6If c takes only values in [0,∞), then it suffices to assume plain measurability ([BS09]). OPTIMAL TRANSPORT AND SKOROKHOD EMBEDDING 7 c-cyclically monotone transport plans resist im”
- Causal optimal transport and its links to enlargement of filtrations and continuous-time stochastic optimization (2016, methodology): “We employ classical arguments, as in [Vil03] or [BS11, Sect.”
- Statistical Aspects of Wasserstein Distances (2018, background): “Very general results (for all Borel cost functions) in this context can be found in Beiglb¨ock & Schachermayer (2011).”