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Optimal transport: discretization and algorithms

Quentin Merigot
Boris Thibert

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.
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hal-02494446 , version 1 (28-02-2020)

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