$C$-cyclical monotonicity as a sufficient criterion for optimality in the multimarginal Monge–Kantorovich problem
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Abstract:
This paper establishes that a generalization of $c$-cyclical monotonicity from the Monge–Kantorovich problem with two marginals gives rise to a sufficient condition for optimality also in the multimarginal version of that problem. To obtain the result, the cost function is assumed to be bounded by a sum of integrable functions. The proof rests on ideas from martingale transport.References
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Additional Information
- Claus Griessler
- Affiliation: Institut für Stochastik und Wirtschaftsmathematik, Technische Universität Wien, 1040 Wien, Austria
- MR Author ID: 1049731
- Received by editor(s): October 16, 2016
- Received by editor(s) in revised form: January 12, 2018
- Published electronically: July 23, 2018
- Additional Notes: This work was financially supported through FWF-projects Y782 and P26736
- Communicated by: Zhen-Qing Chen
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 4735-4740
- MSC (2010): Primary 49K30, 28A35
- DOI: https://doi.org/10.1090/proc/14129
- MathSciNet review: 3856141