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$ C$-cyclical monotonicity as a sufficient criterion for optimality in the multimarginal Monge-Kantorovich problem

Author: Claus Griessler
Journal: Proc. Amer. Math. Soc. 146 (2018), 4735-4740
MSC (2010): Primary 49K30, 28A35
Published electronically: July 23, 2018
MathSciNet review: 3856141
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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.

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Claus Griessler
Affiliation: Institut für Stochastik und Wirtschaftsmathematik, Technische Universität Wien, 1040 Wien, Austria

Keywords: Cyclical monotonicity, mass transport
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
Article copyright: © Copyright 2018 American Mathematical Society