7 Optimal multipartitions

Chapters in this book

1. Frontmatter I
2. Preface V
3. Contents VII
4. How to read this book? XI
5. Notations XIII
6. 1 Introduction 1
7. Part I: Stable marriage and optimal partitions
8. 2 The stable marriage problem 17
9. 3 Many to few: stable partitions 31
10. 4 Monge partitions 39
11. Part II: Multipartitions
12. 5 Weak multipartitions 57
13. 6 Strong multipartitions 71
14. 7 Optimal multipartitions 83
15. 8 Applications to learning theory 103
16. Part III: From optimal partition to optimal transport and back
17. 9 Optimal transport for scalar measures 117
18. 10 Interpolated costs 131
19. Part IV: Cooperative and non-cooperative partitions
20. 11 Back to Monge: individual values 149
21. 12 Sharing the individual value 167
22. 13 Cooperative partitions 177
23. A Convexity 189
24. B Convergence of measures 197
25. Bibliography 203
26. Index 207