A Benamou-Brenier formulation for the multi-marginal optimal transport problem with infimal convolution cost

TL;DR

This paper introduces a dynamic formulation for the multi-marginal optimal transport problem with infimal convolution cost, leveraging Wasserstein barycenters, and relates it to existing dynamical approaches by Pass and Shenfeld.

Contribution

It proposes a novel dynamical formulation for the multi-marginal optimal transport problem using Wasserstein barycenters, connecting it to prior dynamical models.

Findings

Establishes a new dynamical framework for multi-marginal optimal transport

Links the formulation to existing dynamical models by Pass and Shenfeld

Provides theoretical insights into Wasserstein barycenters in this context

Abstract

We present a dynamical version for the multi-marginal optimal transport problem with infimal convolution cost, using the theory of Wasserstein barycentres. We show, how our formulation relates to the dynamical version of the multi-marginal optimal transport problem developed by Pass and Shenfeld (arXiv:2509.22494v2).