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Mixed L 2-Wasserstein Optimal Mapping Between Prescribed Density Functions

Author

Listed:
  • J. D. Benamou

    (INRIA)

  • Y. Brenier

    (Université Paris 6)

Abstract

A time-dependent minimization problem for the computation of a mixed L 2-Wasserstein distance between two prescribed density functions is introduced in the spirit of Ref. 1 for the classical Wasserstein distance. The optimum of the cost function corresponds to an optimal mapping between prescribed initial and final densities. We enforce the final density conditions through a penalization term added to our cost function. A conjugate gradient method is used to solve this relaxed problem. We obtain an algorithm which computes an interpolated L 2-Wasserstein distance between two densities and the corresponding optimal mapping.

Suggested Citation

  • J. D. Benamou & Y. Brenier, 2001. "Mixed L 2-Wasserstein Optimal Mapping Between Prescribed Density Functions," Journal of Optimization Theory and Applications, Springer, vol. 111(2), pages 255-271, November.
    • Handle: RePEc:spr:joptap:v:111:y:2001:i:2:d:10.1023_a:1011926116573
    DOI: 10.1023/A:1011926116573
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    Cited by:

    1. Jean-David Benamou & Guillaume Carlier, 2015. "Augmented Lagrangian Methods for Transport Optimization, Mean Field Games and Degenerate Elliptic Equations," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 1-26, October.

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