Contents

Chapters in this book

1. Frontmatter i
2. Contents vii
3. List of Algorithms xi
4. Foreword xiii
5. Notation Conventions xv
6. Chapter One. Introduction 1
7. Chapter Two. Motivation and Applications 5
8. Chapter Three. Matrix Manifolds: First-Order Geometry 17
9. Chapter Four. Line-Search Algorithms On Manifolds 54
10. Chapter Five. Matrix Manifolds: Second-Order Geometry 91
11. Chapter Six. Newton’s Method 111
12. Chapter Seven. Trust-Region Methods 136
13. Chapter Eight. A Constellation Of Superlinear Algorithms 168
14. A. Elements Of Linear Algebra, Topology, And Calculus 189
15. Bibliography 201
16. Index 221