Replacing positivity constraints by an entropy barrier is popular to approximate solutions of
linear programs. In the special case of the optimal transport problem, this technique dates …

The aim of this article is to show that the Monge–Kantorovich problem is the limit, when a
fluctuation parameter tends down to zero, of a sequence of entropy minimization problems …

Wasserstein gradient flow has emerged as a promising approach to solve optimization
problems over the space of probability distributions. A recent trend is to use the well-known …

Motivated by the occurrence in rate functions of time-dependent large-deviation principles,
we study a class of non-negative functions ℒ that induce a flow, given by ℒ (ρ t, ρ ̇ t)= 0 …

We study the convergence of entropically regularized optimal transport to optimal transport.
The main result is concerned with the convergence of the associated optimizers and takes …

This article details a novel numerical scheme to approximate gradient flows for optimal
transport (ie, Wasserstein) metrics. These flows have proved useful to tackle theoretically …

We investigate the convergence rate of the optimal entropic cost v ε to the optimal transport
cost as the noise parameter ε↓ 0. We show that for a large class of cost functions c on R d× …

We discuss a new notion of distance on the space of finite and nonnegative measures on
Ω⊂\mathbbR^d, which we call the Hellinger--Kantorovich distance. It can be seen as an inf …

In the recent years the Schrödinger problem has gained a lot of attention because of the
connection, in the small-noise regime, with the Monge-Kantorovich optimal transport …

We study the convergence of divergence-regularized optimal transport as the regularization
parameter vanishes. Sharp rates for general divergences including relative entropy or Lp …