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
21 - Duality Theory and Practice
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
The duality theory for linear programs is fully justified in this chapter. It is exploited, in the spirit of robust optimization, to deal with problems from optimal recovery and from compressive sensing, namely with Chebyshev balls computation and owl-norm minimization. Duality results for conic programming, and in particular for semidefinite programming, are also provided without proof.
- Type
- Chapter
- Information
- Mathematical Pictures at a Data Science Exhibition , pp. 177 - 185Publisher: Cambridge University PressPrint publication year: 2022