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Optimal transport: discretization and algorithms

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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Contributor : Quentin Mérigot Connect in order to contact the contributor
Submitted on : Friday, February 28, 2020 - 5:10:37 PM
Last modification on : Wednesday, November 3, 2021 - 8:36:56 AM
Long-term archiving on: : Friday, May 29, 2020 - 5:30:44 PM


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  • HAL Id : hal-02494446, version 1
  • ARXIV : 2003.00855



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



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