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.
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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