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 …

A popular way to solve optimal transport problems numerically is to assume that the source
probability measure is absolutely continuous while the target measure is finitely supported …

This chapter describes techniques for the numerical resolution of optimal transport
problems. We will consider several discretizations of these problems, and we will put a …

We review the construction and analysis of numerical methods for strongly nonlinear PDEs,
with an emphasis on convex and non-convex fully nonlinear equations and the convergence …

We derive nearly tight and non-asymptotic convergence bounds for solutions of entropic
semi-discrete optimal transport. These bounds quantify the stability of the dual solutions of …

Semi-discrete optimal transport problems, which evaluate the Wasserstein distance between
a discrete and a generic (possibly non-discrete) probability measure, are believed to be …

We approximate the regular solutions of the incompressible Euler equations by the solution
of ODEs on finite-dimensional spaces. Our approach combines Arnold's interpretation of the …

We propose a two-scale finite element method for the Monge-Ampère equation with Dirichlet
boundary condition in dimension $ d\ge 2$ and prove that it converges to the viscosity …

We propose a numerical method to find the optimal transport map between a measure
supported on a lower-dimensional subset of R^d and a finitely supported measure. More …

In this work, we consider and compare several different numerical methods to solve the
classic continuous optimal transport problem between two probability densities, while …