# Dynamic characterization of barycentric optimal transport problems and their martingale relaxation

arXiv: https://arxiv.org/abs/2511.21287 · HTML: https://mlsanity.com/paper/2511.21287/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Nov 2025.

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

- [Barycentric Weak Inner-Product Gromov-Wasserstein](https://mlsanity.com/paper/2608.25145/) (2026)

## Abstract (arXiv)

We extend the Benamou-Brenier formula from classical optimal transport to weak optimal transport and show that the barycentric optimal transport problem studied by Gozlan and Juillet has a dynamic analogue. We also investigate a martingale relaxation of this problem, and relate it to the martingale Benamou-Brenier formula of Backhoff-Veraguas, Beiglb"ock, Huesmann and K"allblad.