Optimal Transport: A Semi-discrete Approach 3110633124, 9783110633122

This book focuses on problems at the interplay between the theory of partitions and optimal transport with a view toward

390 129 8MB

English Pages 224 Year 2019

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Optimal Transport: A Semi-discrete Approach
3110633124, 9783110633122

Author / Uploaded
Gershon Wolansky

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

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