Numerical methods for matching for teams and Wasserstein barycenters

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...

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Published inESAIM Mathematical Modelling and Numerical Analysis Vol. 49; no. 6; pp. 1621 - 1642
Main Authors Carlier, Guillaume, Oberman, Adam, Oudet, Edouard
Format Journal Article
LanguageEnglish
Published Les Ulis EDP Sciences 01.11.2015
Société de Mathématiques Appliquées et Industrielles (SMAI) / EDP
SeriesSpecial Issue - Optimal Transport
Subjects
49M29
90C05
Algorithms
Center of gravity
duality
Image processing
Linear programming
Matching
Matching for teams
Mathematics
Numerical methods
numerical methods for nonsmooth convex minimization
Optimization
Optimization and Control
Wasserstein barycenters
matching for teams
linear programming
Wasserstein barycenters
duality
numerical methods for nonsmooth convex minimization
Online AccessGet full text
ISSN0764-583X
2822-7840
1290-3841
1290-3841
2804-7214
DOI10.1051/m2an/2015033

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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.
AbstractList 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.
Author Oberman, Adam
Carlier, Guillaume
Oudet, Edouard
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  surname: Carlier
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  organization: CEREMADE, UMR CNRS 7534, Université Paris IX Dauphine, Pl. de Lattre de Tassigny, 75775 Paris cedex 16, France
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  givenname: Adam
  surname: Oberman
  fullname: Oberman, Adam
  organization: Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, Canada
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  givenname: Edouard
  surname: Oudet
  fullname: Oudet, Edouard
  organization: Laboratoire Jean Kuntzmann, Université Joseph Fourier, Tour IRMA, BP 53 51, rue des Mathématiques 38041 Grenoble cedex 9, France
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10.1109/TIP.2010.2052822
10.1137/100805741
10.1007/978-3-642-24785-9_37
10.1007/978-3-540-71050-9
10.1090/gsm/058
10.1007/s00199-008-0415-z
10.1016/j.jcp.2013.12.015
10.3934/dcds.2014.34.1623
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Issue 6
Keywords matching for teams
linear programming
Wasserstein barycenters
duality
numerical methods for nonsmooth convex minimization
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Snippet Equilibrium multi-population matching (matching for teams) is a problem from mathematical economics which is related to multi-marginal optimal transport. A...
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SubjectTerms 49M29
90C05
Algorithms
Center of gravity
duality
Image processing
Linear programming
Matching
Matching for teams
Mathematics
Numerical methods
numerical methods for nonsmooth convex minimization
Optimization
Optimization and Control
Wasserstein barycenters
Title Numerical methods for matching for teams and Wasserstein barycenters
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