Computational optimal transport: With applications to data science
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 …
mathematician Gaspard Monge (1746–1818): A worker with a shovel in hand has to move a …
Convergence of a Newton algorithm for semi-discrete optimal transport
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 …
probability measure is absolutely continuous while the target measure is finitely supported …
Optimal transport: discretization and algorithms
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 …
problems. We will consider several discretizations of these problems, and we will put a …
Numerical analysis of strongly nonlinear PDEs
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 …
with an emphasis on convex and non-convex fully nonlinear equations and the convergence …
Nearly tight convergence bounds for semi-discrete entropic optimal transport
A Delalande - International Conference on Artificial …, 2022 - proceedings.mlr.press
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. These bounds quantify the stability of the dual solutions of …
Semi-discrete optimal transport: Hardness, regularization and numerical solution
B Taşkesen, S Shafieezadeh-Abadeh… - Mathematical Programming, 2023 - Springer
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 …
a discrete and a generic (possibly non-discrete) probability measure, are believed to be …
A Lagrangian scheme à la Brenier for the incompressible Euler equations
TO Gallouët, Q Mérigot - Foundations of Computational Mathematics, 2018 - Springer
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 …
of ODEs on finite-dimensional spaces. Our approach combines Arnold's interpretation of the …
Two-scale method for the Monge-Ampère equation: convergence to the viscosity solution
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 …
boundary condition in dimension $ d\ge 2$ and prove that it converges to the viscosity …
An algorithm for optimal transport between a simplex soup and a point cloud
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 …
supported on a lower-dimensional subset of R^d and a finitely supported measure. More …
Techniques for continuous optimal transport problem
L Dieci, D Omarov - Computers & Mathematics with Applications, 2023 - Elsevier
In this work, we consider and compare several different numerical methods to solve the
classic continuous optimal transport problem between two probability densities, while …
classic continuous optimal transport problem between two probability densities, while …