Optimal transport: discretization and algorithms

Quentin Merigot (1) , Boris Thibert (2)

1 LMO - Laboratoire de Mathématiques d'Orsay
2 CVGI - Calcul des Variations, Géométrie, Image

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.

Domaines: Analyse numérique [math.NA]; Optimisation et contrôle [math.OC]

Quentin Merigot, Boris Thibert. Optimal transport: discretization and algorithms. 2020. ⟨hal-02494446⟩