论文标题
最佳运输简介
A Brief on Optimal Transport
论文作者
论文摘要
演示文稿涵盖了拓扑和测量理论的先决条件。然后是对耦合和最佳运输基本定义的介绍。然后引入了Kantrorovich问题，并提出了存在定理。遵循最佳运输设置后，简要概述了Wasserstein距离，并简短地证明了它如何计量紧凑型域上的概率度量空间。本演讲是对维拉尼（Villani）的“最佳运输：旧和新的”第1-4章和第6章的一部分的详细检查。
The presentation covers prerequisite results from Topology and Measure Theory. This is then followed by an introduction into couplings and basic definitions for optimal transport. The Kantrorovich problem is then introduced and an existence theorem is presented. Following the setup of optimal transport is a brief overview of the Wasserstein distance and a short proof of how it metrizes the space of probability measures on a COMPACT domain. This presentation is a detailed examination of Villani's "Optimal Transport: Old and New" chapters 1-4 and part of 6.
