$c$-cyclical monotonicity as a sufficient criterion for optimality in the multi-marginal Monge-Kantorovich problem

Claus Griessler

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arXiv · 1601.05608

$c$-cyclical monotonicity as a sufficient criterion for optimality in the multi-marginal Monge-Kantorovich problem

Claus Griessler

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Abstract

This note 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 multi-marginal 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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BibTeX RIS

Claus Griessler. 2016-01-21. $c$-cyclical monotonicity as a sufficient criterion for optimality in the multi-marginal Monge-Kantorovich problem. https://arxiv.org/abs/1601.05608

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