论文标题
同时最佳运输
Simultaneous Optimal Transport
论文作者
论文摘要
我们提出了矢量值措施之间的质量运输的一般框架，这将称为同时最佳运输（SOT）。新框架是由于需要同时运输不同类型的资源，即单一旅行，从指定的起源到目的地。同样，在经济匹配中，一个需要同时将不同商品的供应和需求等同于两组，例如买卖双方。同时运输的数学结构与最佳运输的经典环境大不相同，这导致了许多新的挑战。 Monge和Kantorovich配方对比并连接。建立了存在条件和二元公式。更有趣的是，通过将SOT连接到Martingale Optimal Transport（MOT）的自然放松，我们引入了Mot-Sot Price，该均可在许多有趣的情况下可以明确的SOT解决方案。
We propose a general framework of mass transport between vector-valued measures, which will be called simultaneous optimal transport (SOT). The new framework is motivated by the need to transport resources of different types simultaneously, i.e., in single trips, from specified origins to destinations; similarly, in economic matching, one needs to couple two groups, e.g., buyers and sellers, by equating supplies and demands of different goods at the same time. The mathematical structure of simultaneous transport is very different from the classic setting of optimal transport, leading to many new challenges. The Monge and Kantorovich formulations are contrasted and connected. Existence conditions and duality formulas are established. More interestingly, by connecting SOT to a natural relaxation of martingale optimal transport (MOT), we introduce the MOT-SOT parity, which allows for explicit solutions of SOT in many interesting cases.
