A dynamical formulation of multi-marginal optimal transport
Optimization and Control
2025-10-14 v2 Analysis of PDEs
Probability
Abstract
We present a primal-dual dynamical formulation of the multi-marginal optimal transport problem for (semi-)convex cost functions. Even in the two-marginal setting, this formulation applies to cost functions not covered by the classical dynamical approach of Benamou-Brenier. Our dynamical formulation yields a convex optimization problem, enabling the use of convex optimization tools to find quasi-Monge solutions of the static multi-marginal problem for translation-invariant costs. We illustrate our results numerically with proximal splitting methods.
Cite
@article{arxiv.2509.22494,
title = {A dynamical formulation of multi-marginal optimal transport},
author = {Brendan Pass and Yair Shenfeld},
journal= {arXiv preprint arXiv:2509.22494},
year = {2025}
}