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Numerical methods for matching for teams and Wasserstein barycenters

Abstract : Equilibrium multi-population matching (matching for teams) is a problem from mathematical economics which is related to multi-marginal optimal transport. A special but important case is the Wasserstein barycenter problem, which has applications in image processing and statistics. Two algorithms are presented: a linear programming algorithm and an efficient nonsmooth optimization algorithm, which applies in the case of the Wasserstein barycenters. The measures are approximated by discrete measures: convergence of the approximation is proved. Numerical results are presented which illustrate the efficiency of the algorithms.
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Preprints, Working Papers, ...
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Contributor : Jean-David Benamou Connect in order to contact the contributor
Submitted on : Monday, February 2, 2015 - 2:34:31 PM
Last modification on : Thursday, October 7, 2021 - 10:23:33 AM

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  • HAL Id : hal-01112224, version 1
  • ARXIV : 1411.3602


Guillaume Carlier, Edouard Oudet, Adam Oberman. Numerical methods for matching for teams and Wasserstein barycenters. 2015. ⟨hal-01112224⟩



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