Approximation of Monge-Kantorovich Problems


Optimal transportation of substances, goods, or information is a classical mathematical problem with applications in economics, meteorology, and computer science. It can be formulated as a high-dimensional linear program whose direct solution is difficult. More efficient approaches are based on equivalent continuous formulations via partial differential equations or variational problems. These are nonlinear and nondifferentiable mathematical problems that require a suitable discretization and iterative solution. The project focuses on the development and numerical analysis of finite element discretizations, the automatic efficient mesh refinement based on rigorous a posteriori error estimates, and the fast iterative solution. Special emphasis is on the avoidance of regularizations and use of unjustified smoothness assumptions on solutions.


No publications from this project yet.


Sören Bartel, Gerd Wachsmuth: Numerical Approximation of Optimal Convex Shapes (SPP1962-089, 10/2018, [bib])

Sören Bartels, Lars Diening, Ricardo Nochetto: Unconditional Stability of Semi-Implicit Discretizations of Singular Flows (SPP1962-045, 11/2017, [bib])

Sören Bartels, Patrick Schön: Adaptive Approximation of the Monge--Kantorovich Problem via Primal-Dual Gap Estimates (SPP1962-037, 10/2017, [bib])

Sören Bartels, Stephan Hertzog: Error Bounds for Discretized Optimal Transport and its Reliable Efficient Numerical Solution (SPP1962-035, 10/2017, [bib])

Sören Bartels, Giuseppe Buttazzo: Numerical Solution of a Nonlinear Eigenvalue Problem Arising in Optimal Insulation (SPP1962-032, 08/2017, [bib])


  • member's portrait

    Prof. Sören Bartels

    Albert-Ludwigs-Universität Freiburg
    Principal Investigator
  • member's portrait

    Zhangxian Wang

    Albert-Ludwigs-Universität Freiburg
    Research Assistant
  • member's portrait

    Dr. Andrea Bonito

    Texas A&M University
    Cooperation Partner
  • member's portrait

    Dr. Max Jensen

    University of Sussex
    Cooperation Partner
  • member's portrait

    Prof. Ricardo H. Nochetto

    University of Maryland
    Cooperation Partner

Project Related News

  • Oct 25, 2018 : New preprint submitted

    Gerd Wachsmuth submitted the preprint SPP1962-089, Numerical Approximation of Optimal Convex Shapes

  • Oct 10, 2016 : Welcome to our new project member

    Zhangxian Wang joins project 1.