English

On the geometry and dynamical formulation of the Sinkhorn algorithm for optimal transport

Numerical Analysis 2025-08-12 v2 Numerical Analysis Differential Geometry

Abstract

The Sinkhorn algorithm is a numerical method for the solution of optimal transport problems. Here, I give a brief survey of this algorithm, with a strong emphasis on its geometric origin: it is natural to view it as a discretization, by standard methods, of a non-linear integral equation. In the appendix, I also provide a short summary of an early result of Beurling on product measures, directly related to the Sinkhorn algorithm.

Keywords

Cite

@article{arxiv.2309.09089,
  title  = {On the geometry and dynamical formulation of the Sinkhorn algorithm for optimal transport},
  author = {Klas Modin},
  journal= {arXiv preprint arXiv:2309.09089},
  year   = {2025}
}

Comments

10 pages, 1 figure