Optimal Transport: A Semi-Discrete Approach

Gershon Wolansky

Published by De Gruyter 2021

Optimal Transport

A Semi-Discrete Approach

Gershon Wolansky

Volume 37 in the series De Gruyter Series in Nonlinear Analysis and Applications

https://doi.org/10.1515/9783110635485

Overview
Contents

About this book

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.

Presents optimal transport with a view toward applications in game theory and economics
Covers the interplay between the theory of partitions and optimal transport
Of interest to researchers and graduate students in applied mathematics

Author / Editor information

Gershon Wolansky, Technion - Israel Institute of Technology, Israel.

Topics

Frontmatter Publicly Available Download PDF	I
Preface Publicly Available Download PDF	V
Contents Publicly Available Download PDF	VII
How to read this book? Publicly Available Download PDF	XI
Notations Publicly Available Download PDF	XIII
1 Introduction Requires Authentication Unlicensed Licensed Download PDF	1
Part I: Stable marriage and optimal partitions
2 The stable marriage problem Requires Authentication Unlicensed Licensed Download PDF	17
3 Many to few: stable partitions Requires Authentication Unlicensed Licensed Download PDF	31
4 Monge partitions Requires Authentication Unlicensed Licensed Download PDF	39
Part II: Multipartitions
5 Weak multipartitions Requires Authentication Unlicensed Licensed Download PDF	57
6 Strong multipartitions Requires Authentication Unlicensed Licensed Download PDF	71
7 Optimal multipartitions Requires Authentication Unlicensed Licensed Download PDF	83
8 Applications to learning theory Requires Authentication Unlicensed Licensed Download PDF	103
Part III: From optimal partition to optimal transport and back
9 Optimal transport for scalar measures Requires Authentication Unlicensed Licensed Download PDF	117
10 Interpolated costs Requires Authentication Unlicensed Licensed Download PDF	131
Part IV: Cooperative and non-cooperative partitions
11 Back to Monge: individual values Requires Authentication Unlicensed Licensed Download PDF	149
12 Sharing the individual value Requires Authentication Unlicensed Licensed Download PDF	167
13 Cooperative partitions Requires Authentication Unlicensed Licensed Download PDF	177
A Convexity Requires Authentication Unlicensed Licensed Download PDF	189
B Convergence of measures Requires Authentication Unlicensed Licensed Download PDF	197
Bibliography Requires Authentication Unlicensed Licensed Download PDF	203
Index Requires Authentication Unlicensed Licensed Download PDF	207

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Researchers and graduate students in mathematical analysis and applied mathematics.
Pages
- Front matter: 14
- Main content: 210
Illustrations
- Illustrations: 10
Keywords: Monge-Kantorovič-Transportproblem; Transportproblem

eBook

Published: January 18, 2021
ISBN: 9783110635485

Hardcover

Published: January 18, 2021
ISBN: 9783110633122