Convergence Rates for Discretized Monge–Ampère Equations and Quantitative Stability of Optimal Transport
Artikel i vetenskaplig tidskrift, 2021

In recent works-both experimental and theoretical-it has been shown how to use computational geometry to efficiently construct approximations to the optimal transport map between two given probability measures on Euclidean space, by discretizing one of the measures. Here we provide a quantitative convergence analysis for the solutions of the corresponding discretized Monge-Ampere equations. This yields H-1-converge rates, in terms of the corresponding spatial resolution h, of the discrete approximations of the optimal transport map, when the source measure is discretized and the target measure has bounded convex support. Periodic variants of the results are also established. The proofs are based on new quantitative stability results for optimal transport maps, shown using complex geometry.

Optimal transport

Numerical analysis

Complex differential geometry

Monge-Ampere equations


Robert Berman

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Algebra och geometri

Foundations of Computational Mathematics

1615-3375 (ISSN) 1615-3383 (eISSN)

Vol. 21 4 1099-1140



Annan fysik

Matematisk analys



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