Semidefinite Optimization and Convex Algebraic Geometry
$150.00 (P)
Part of MPS-SIAM Series on Optimization
- Editors:
- Grigoriy Blekherman, Georgia Institute of Technology
- Pablo A. Parrilo, Massachusetts Institute of Technology
- Rekha Thomas, University of Washington
- Date Published: March 2013
- availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
- format: Paperback
- isbn: 9781611972283
$
150.00
(P)
Paperback
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This book provides a self-contained, accessible introduction to the mathematical advances and challenges resulting from the use of semidefinite programming in polynomial optimization. This important and highly applicable research area with contributions from convex geometry, algebraic geometry, and optimization is known as convex algebraic geometry. Each chapter addresses a fundamental aspect of the topic, beginning with an introduction to nonnegative polynomials and sums of squares, and their connections to semidefinite programming. The material quickly advances to areas at the forefront of current research, including semidefinite representability of convex sets, duality theory in algebraic geometry, and nontraditional topics such as sums of squares of complex forms. The book is a suitable entry point to the subject for readers at the graduate level or above in mathematics, engineering or computer science. Instructors will find the book appropriate for a class or seminar, and researchers will encounter open problems and new research directions.
Read more- An accessible introduction to a powerful and quickly evolving area of optimization
- Suitable for a class or seminar course, with exercises aimed at aiding beginners' understanding of the topic
- A guide to the necessary background material is provided in an appendix
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×Product details
- Date Published: March 2013
- format: Paperback
- isbn: 9781611972283
- length: 495 pages
- dimensions: 254 x 177 x 24 mm
- weight: 0.89kg
- availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
Table of Contents
List of contributors
List of figures
Preface
List of notation
1. What is convex algebraic geometry? Grigoriy Blekherman, Pablo A. Parrilo and Rekha R. Thomas
2. Semidefinite optimization Pablo A. Parrilo
3. Polynomial optimization, sums of squares, and applications Pablo A. Parrilo
4. Nonnegative polynomials and sums of squares Grigoriy Blekherman
5. Dualities Philipp Rostalski and Bernd Sturmfels
6. Semidefinite representability Jiawang Nie
7. Convex hulls of algebraic sets João Gouveia and Rekha R. Thomas
8. Free convexity J. William Helton, Igor Klep and Scott McCullough
9. Sums of Hermitian squares: old and new Mihai Putinar
Appendix A. Background material Grigoriy Blekherman, Pablo A. Parrilo and Rekha R. Thomas
Index.
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