# Entropic approximation of $\infty$-optimal transport problems

## TL;DR

This paper introduces an entropic approximation method for supremal cost optimal transport problems, proving convergence to $ty$-cyclically monotone plans and demonstrating numerical results with Sinkhorn's algorithm.

## Contribution

It develops a novel entropic penalization approach for $ty$-optimal transport problems, establishing $ extGamma$-convergence and plan selection properties.

## Key findings

- Proves $ extGamma$-convergence of the entropic approximation.
- Shows the method selects $ty$-cyclically monotone plans.
- Provides numerical illustrations using Sinkhorn's algorithm.

## Abstract

We propose an entropic approximation approach for optimal transportation problems with a supremal cost. We establish $\Gamma$-convergence for suitably chosen parameters for the entropic penalization and that this procedure selects $\infty$-cyclically monotone plans at the limit. We also present some numerical illustrations performed with Sinkhorn's algorithm.