ON THE GEOMETRY AND DYNAMICAL FORMULATION OF THE SINKHORN ALGORITHM FOR OPTIMAL TRANSPORT
Journal article, 2024

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.

product measures

Sinkhorn algorithm

groups of diffeomorphisms

Beurling

Madelung transform

Schrodinger bridge

geometric hydrodynamics

Optimal transport

Author

Klas Modin

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Journal of Computational Dynamics

2158-2491 (ISSN) 2158-2505 (eISSN)

Vol. 11 4 442-452

Long-time 2D hydrodynamics via quantization

Swedish Research Council (VR) (2022-03453), 2023-01-01 -- 2026-12-31.

Subject Categories

Mechanical Engineering

Mathematics

Other Engineering and Technologies

DOI

10.3934/jcd.2024006

More information

Latest update

9/23/2024