Optimal transport: discretization and algorithms

  title={Optimal transport: discretization and algorithms},
  author={Quentin M{\'e}rigot and Boris Thibert},
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… Expand
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  • Q. Mérigot
  • Mathematics, Computer Science
  • Comput. Graph. Forum
  • 2011
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  • Bernhard Schmitzer
  • Mathematics, Computer Science
  • Journal of Mathematical Imaging and Vision
  • 2016
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  • R. Berman
  • Computer Science, Mathematics
  • Found. Comput. Math.
  • 2021
A quantitative convergence analysis for the solutions of the corresponding discretized Monge–Ampère equations yields convergence rates of the discrete approximations of the optimal transport map, when the source measure is discretization and the target measure has bounded convex support. Expand
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  • Mathematics, Computer Science
  • Numerische Mathematik
  • 2020
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