Preconditioning of optimal transport

Max Kuang, Estebang Tabak

Research output: Contribution to journalArticle

Abstract

A preconditioning procedure is developed for the L2 and more general optimal transport problems. The procedure is based on a family of affine map pairs which transforms the original measures into two new measures that are closer to each other while preserving the optimality of solutions. It is proved that the preconditioning procedure minimizes the remaining transportation cost among all admissible affine maps. The procedure can be used on both continuous measures and finite sample sets from distributions. In numerical examples, the procedure is applied to multivariate normal distributions, to a two-dimensional shape transform problem, and to color-transfer problems.

Original languageEnglish (US)
Pages (from-to)A1793-A1810
JournalSIAM Journal on Scientific Computing
Volume39
Issue number4
DOIs
StatePublished - 2017

Keywords

  • Matrix factorization
  • Optimal transport
  • Preconditioning

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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