Optimal transport (OT) theory can be informally described using the words of the French
mathematician Gaspard Monge (1746–1818): A worker with a shovel in hand has to move a …

Optimal transport maps between two probability distributions $\mu $ and $\nu $ on $\R^ d $
have found extensive applications in both machine learning and statistics. In practice, these …

We consider the pricing problem faced by a revenue-maximizing platform matching price-
sensitive customers to flexible supply units within a geographic area. This can be interpreted …

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 …

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 …

This paper presents a systematic existence and uniqueness theory of weak measure
solutions for systems of non-local interaction PDEs with two species, which are the PDE …

Gradient flows in the Wasserstein space have become a powerful tool in the analysis of
diffusion equations, following the seminal work of Jordan, Kinderlehrer and Otto (JKO). The …

Carbon emission trading achieves both economic and environmental benefits. The
imbalance between quota supply and demand restricts the development of the carbon …

The article discusses the issue of modelling traffic flows and the transport network. Faced
with an increase in the number of vehicles in road networks, the problem of congestion and …

A recent paper by Cordero-Erausquin and Klartag provides a characterization of the
measures μ on R d which can be expressed as the moment measures of suitable convex …