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Griessler, C. (2016). c-cyclical monotonicity as a sufficient criterion for optimality in the multi-marginal Monge-Kantorovich problem. arXiv. https://doi.org/10.48550/arXiv.1601.05608
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.