NUMERICAL METHODS FOR MATCHING FOR TEAMS AND WASSERSTEIN BARYCENTERS

NUMERICAL METHODS FOR MATCHING FOR TEAMS AND WASSERSTEIN BARYCENTERS
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DOI：
10.1051/m2an/2015033
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发表时间：
2015-11-01
期刊：
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
影响因子：
--
通讯作者：
Oudet, Edouard
Oudet, Edouard
中科院分区：
其他
文献类型：
--
作者：
Carlier, Guillaume;Oberman, Adam;Oudet, Edouard

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多种群均衡匹配（团队匹配）是一个与多边际最优运输相关的数理经济学问题。一个特殊但重要的情况是瓦瑟斯坦重心问题，它在图像处理和统计中有应用。提出了两种算法：一个线性规划算法和一个有效的非光滑优化算法，它适用于Wasserstein重心的情况。的措施是近似的离散措施：收敛性的近似证明。数值结果表明了算法的有效性。
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.