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摘要翻译：
在当前的书中，我建议一个关于最佳交通的越野路径。我尽量避免先前的分析知识，PDE理论和功能分析。因此，我专注于离散和半离散的情况，并且总是假定底层空间是紧的。然而，一些测度理论和凸性的基本知识是不可避免的。为了使它尽可能自成一体，我包括了一个附有一些基本定义和结果的附录。我相信任何数学专业的研究生，以及高年级的本科生，都能读懂这本书。有些章节（特别是第二部分和第三部分）对专家来说也很有趣。从最基本的、完全离散的问题开始，我试图把最优运输作为著名的稳定婚姻问题的一个特例。从那里我们继续到划分问题，它可以表述为从连续空间到离散空间的传输。本文还介绍了信息论和博弈论（合作和非合作）的应用。最后，将两紧致测度空间之间传输的一般情况引入为两半离散传输之间的耦合。
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英文标题：
《Semi-discrete optimal transport》
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作者：
Gershon Wolansky
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最新提交年份：
2020
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分类信息：
一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Computer Science 计算机科学
二级分类：Information Theory 信息论
分类描述：Covers theoretical and experimental aspects of information theory and coding. Includes material in ACM Subject Class E.4 and intersects with H.1.1.
涵盖信息论和编码的理论和实验方面。包括ACM学科类E.4中的材料，并与H.1.1有交集。
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一级分类：Economics 经济学
二级分类：Theoretical Economics 理论经济学
分类描述：Includes theoretical contributions to Contract Theory, Decision Theory, Game Theory, General Equilibrium, Growth, Learning and Evolution, Macroeconomics, Market and Mechanism Design, and Social Choice.
包括对契约理论、决策理论、博弈论、一般均衡、增长、学习与进化、宏观经济学、市场与机制设计、社会选择的理论贡献。
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一级分类：Mathematics 数学
二级分类：Information Theory 信息论
分类描述：math.IT is an alias for cs.IT. Covers theoretical and experimental aspects of information theory and coding.
它是cs.it的别名。涵盖信息论和编码的理论和实验方面。
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英文摘要：
In the current book I suggest an off-road path to the subject of optimal transport. I tried to avoid prior knowledge of analysis, PDE theory and functional analysis, as much as possible. Thus I concentrate on discrete and semi-discrete cases, and always assume compactness for the underlying spaces. However, some fundamental knowledge of measure theory and convexity is unavoidable. In order to make it as self-contained as possible I included an appendix with some basic definitions and results. I believe that any graduate student in mathematics, as well as advanced undergraduate students, can read and understand this book. Some chapters (in particular in Parts II\&III ) can also be interesting for experts. Starting with the the most fundamental, fully discrete problem I attempted to place optimal transport as a particular case of the celebrated stable marriage problem. From there we proceed to the partition problem, which can be formulated as a transport from a continuous space to a discrete one. Applications to information theory and game theory (cooperative and non-cooperative) are introduced as well. Finally, the general case of transport between two compact measure spaces is introduced as a coupling between two semi-discrete transports.
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PDF链接：
https://arxiv.org/pdf/1911.04348
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