Optimal Transport: A Semi-discrete Approach

✍ Scribed by Gershon Wolansky

• Publisher: de Gruyter
• Year: 2019
• Tongue: English
• Leaves: 224
• Series: De Gruyter Series in Nonlinear Analysis and Applications
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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