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

Griessler, Claus

doi:10.1090/proc/14129

$C$-cyclical monotonicity as a sufficient criterion for optimality in the multimarginal Monge–Kantorovich problem
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Proc. Amer. Math. Soc. 146 (2018), 4735-4740 Request permission

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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