Partial L1 Monge-Kantorovich problem: Variational formulation and numerical approximation

John W. Barrett, Leonid Prigozhin

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

We consider the Monge-Kantorovich problem with transportation cost equal to distance and a relaxed mass balance condition: instead of optimally transporting one given distribution of mass onto another with the same total mass, only a given amount of mass, m, has to be optimally transported. In this partial problem the given distributions are allowed to have different total masses and m should not exceed the least of them. We derive and analyze a variational formulation of the arising free boundary problem in optimal transportation. Furthermore, we introduce and analyse the finite element approximation of this formulation using the lowest order Raviart-Thomas element. Finally, we present some numerical experiments where both approximations to the optimal transportation domains and the optimal transport between them are computed.

Original languageEnglish
Pages (from-to)201-238
Number of pages38
JournalInterfaces and Free Boundaries
Volume11
Issue number2
DOIs
StatePublished - 1 Jan 2009

Keywords

  • Augmented Lagrangian
  • Convergence analysis
  • Finite elements
  • Free boundary
  • Monge-Kantorovich problem
  • Optimal transportation
  • Variational formulation

ASJC Scopus subject areas

  • Surfaces and Interfaces

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