Optimal Transport
A Semi-Discrete Approach
1st Edition
Published on 18. January 2021
XIV, 210 pages
978-3-11-063548-5 (ISBN)
Description
This book focuses on problems at the interplay between the theory of partitions and optimal transport with a view toward applications. Topics covered include problems related to stable marriages and stable partitions, multipartitions, optimal transport for measures and optimal partitions, and finally cooperative and noncooperative partitions. All concepts presented are illustrated by examples from game theory, economics, and learning.
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01/2021
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De Gruyter
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Person
Gershon Wolansky
, Technion - Israel Institute of Technology, Israel.
Content
- Intro
- Preface
- Contents
- How to read this book?
- Notations
- 1 Introduction
- Part I: Stable marriage and optimal partitions
- 2 The stable marriage problem
- 3 Many to few: stable partitions
- 4 Monge partitions
- Part II: Multipartitions
- 5 Weak multipartitions
- 6 Strong multipartitions
- 7 Optimal multipartitions
- 8 Applications to learning theory
- Part III: From optimal partition to optimal transport and back
- 9 Optimal transport for scalar measures
- 10 Interpolated costs
- Part IV: Cooperative and non-cooperative partitions
- 11 Back to Monge: individual values
- 12 Sharing the individual value
- 13 Cooperative partitions
- A Convexity
- B Convergence of measures
- Bibliography
- Index
