Abstract

In this talk, staying in the discrete setting, we will first introduce the Monge-Kantorovitch problem, which is the central problem in optimal transport. After this, we will say a few words about a functional called ”entropy” (with a generalized version of it) and present its properties. This will then allow us to discuss an entropically penalized version of the Monge-Kantorovitch problem and provide some numerical illustrations of the results/interpretations presented hereafter. I will finally discuss the issues arising when we try to generalize the presented results in the non-discrete setting.

Keywords: Optimal transport - Entropy - Sinkhorn algorithm - Convergence in probability spaces.