Optimal transportation theory is an area of mathematics with real‐world applications in fields ranging from economics to optimal control to machine learning. We propose a new algorithm for solving discrete transport (network flow) problems, based on classical auction methods. Auction methods were originally developed as an alternative to the Hungarian method for the assignment problem, so the classic auction‐based algorithms solve integer‐valued optimal transport by converting such problems into assignment problems. The general transport auction method we propose works directly on real‐valued transport problems. Our results prove termination, bound the transport error, and relate our algorithm to the classic algorithms of Bertsekas and Castañón.

中文翻译：

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一种用于优化运输的实值拍卖算法

最优运输理论是数学领域，在经济学，最优控制到机器学习等领域都有实际应用。我们基于经典拍卖方法，提出了一种解决离散运输（网络流）问题的新算法。拍卖方法最初是作为匈牙利分配方法的替代方法而开发的，因此基于拍卖的经典算法通过将此类问题转换为分配问题来解决整数值的最优运输。我们建议的一般运输拍卖方法直接适用于实值运输问题。我们的结果证明了终止，限制了运输错误，并将我们的算法与Bertsekas和Castañón的经典算法相关联。