Journal Articles Journal of the European Mathematical Society Year : 2019

Convergence of a Newton algorithm for semi-discrete optimal transport

Abstract

Many problems in geometric optics or convex geometry can be recast as optimal transport problems and a popular way to solve these problems numerically is to assume that the source probability measure is absolutely continuous while the target measure is finitely supported. We introduce a damped Newton's algorithm for this type of problems, which is experimentally efficient, and we establish its global linear convergence for cost functions satisfying an assumption that appears in the regularity theory for optimal transport.
Fichier principal
Vignette du fichier
ma.pdf (1) Télécharger le fichier
Origin Files produced by the author(s)
Loading...

Dates and versions

hal-01290496 , version 1 (18-03-2016)

Identifiers

Cite

Jun Kitagawa, Quentin Mérigot, Boris Thibert. Convergence of a Newton algorithm for semi-discrete optimal transport. Journal of the European Mathematical Society, 2019, 21 (9), pp.2603-2651. ⟨10.4171/JEMS/889⟩. ⟨hal-01290496⟩
705 View
280 Download

Altmetric

Share

More