Entropic Approximation of $$\infty $$-Optimal Transport Problems

Abstract

We propose an entropic approximation approach for optimal transportation problems with a supremal cost. We establish $$\Gamma $$ Γ -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.