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Optimal transport: discretization and algorithms

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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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