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

arXiv: https://arxiv.org/abs/1601.05608 · HTML: https://mlsanity.com/paper/1601.05608/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jan 2016.

## Built on by (most cited first, 1 of 1)

- [A Unified Kantorovich Duality for Multimarginal Optimal Transport](https://mlsanity.com/paper/2601.17171/) (2026)

## Abstract (arXiv)

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.