Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Notation
- Part One Machine Learning
- Part Two Optimal Recovery
- Part Three Compressive Sensing
- Part Four Optimization
- Executive Summary
- 19 Basic Convex Optimization
- 20 Snippets of Linear Programming
- 21 Duality Theory and Practice
- 22 Semidefinite Programming in Action
- 23 Instances of Nonconvex Optimization
- Part Five Neural Networks
- Appendices
- References
- Index
22 - Semidefinite Programming in Action
from Part Four - Optimization
Published online by Cambridge University Press: 21 April 2022
- Frontmatter
- Dedication
- Contents
- Preface
- Notation
- Part One Machine Learning
- Part Two Optimal Recovery
- Part Three Compressive Sensing
- Part Four Optimization
- Executive Summary
- 19 Basic Convex Optimization
- 20 Snippets of Linear Programming
- 21 Duality Theory and Practice
- 22 Semidefinite Programming in Action
- 23 Instances of Nonconvex Optimization
- Part Five Neural Networks
- Appendices
- References
- Index
Summary
This chapter examines an Lp-minimization program with interpolatory constraints as a way to introduce techniques commonly used in semidefinite programming. The case p = 2 reveals a link between positive semidefiniteness and Schur complements. The case p = ? illustrates the sum-of-squares techniques in connection with Riesz-Fejér theorem. The case p = 1 illustrates the method of moments in connection with the discrete trigonometric moment problem.
- Type
- Chapter
- Information
- Mathematical Pictures at a Data Science Exhibition , pp. 186 - 193Publisher: Cambridge University PressPrint publication year: 2022