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

2023/09/16 by Modin, Klas
#35Q49 #37K65 #49Q22 #65R20 #Differential Geometry (math.DG) #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2309.09089

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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