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
2158-2505 (eISSN)
Vol. 11 4 442-452Long-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