# 60 years of cyclic monotonicity: a survey

arXiv: https://arxiv.org/abs/2308.07682 · HTML: https://mlsanity.com/paper/2308.07682/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Aug 2023.

## Built on by (most cited first, 2 of 2)

- [What is a good matching of probability measures? A counterfactual lens on transport maps](https://mlsanity.com/paper/2509.16027/) (2025)
- [BalLOT: Balanced k-means clustering with optimal transport](https://mlsanity.com/paper/2512.05926/) (2025)

## Abstract (arXiv)

The primary purpose of this note is to provide an instructional summary of the state of the art regarding cyclic monotonicity and related notions. We will also present how these notions are tied to optimality in the optimal transport (or Monge-Kantorovich) problem.