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
23 - Instances of Nonconvex Optimization
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 presents three examples of nonconvex optimization programs that can be solved (almost) exactly. The first example concerns quadratically constrained quadratic programs, whose treatment relies on the so-called S-lemma. The second example is dynamic programming, which is utilized to compute best approximants by sparse and disjointed vectors. The third example consists of projected gradient descent algorithms, including iterative hard thresholding algorithms.
- Type
- Chapter
- Information
- Mathematical Pictures at a Data Science Exhibition , pp. 194 - 204Publisher: Cambridge University PressPrint publication year: 2022