Optimal transport: discretization and algorithms
Numerical Analysis
2020-03-03 v1 Numerical Analysis
Optimization and Control
Abstract
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 strong focus on the mathematical analysis of the algorithms to solve the discretized problems. We will describe in detail the following discretizations and corresponding algorithms: the assignment problem and Bertsekas auction's algorithm; the entropic regularization and Sinkhorn-Knopp's algorithm; semi-discrete optimal transport and Oliker-Prussner or damped Newton's algorithm, and finally semi-discrete entropic regularization. Our presentation highlights the similarity between these algorithms and their connection with the theory of Kantorovich duality.
Cite
@article{arxiv.2003.00855,
title = {Optimal transport: discretization and algorithms},
author = {Quentin Merigot and Boris Thibert},
journal= {arXiv preprint arXiv:2003.00855},
year = {2020}
}