团队匹配的数值方法与Wasserstein均值中心
Numerical methods for matching for teams and Wasserstein barycenters
AI总结：
本文提出两种算法用于团队匹配问题及Wasserstein均值中心问题，通过离散化措施并证明其收敛性，展示算法效率。
摘要：
均衡多群体匹配（团队匹配）是数学经济学中的问题，与多边际最优运输相关。Wasserstein均值中心问题是其特殊但重要的情况，应用于图像处理和统计学。本文提出线性规划算法和高效非光滑优化算法，用于Wasserstein均值中心问题。措施通过离散措施近似：证明了近似的收敛性。展示了数值结果，以说明算法的效率。
英文摘要：
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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