An Introduction to Polynomial and Semi-Algebraic Optimization
£43.99
Part of Cambridge Texts in Applied Mathematics
- Author: Jean Bernard Lasserre, Centre National de la Recherche Scientifique (CNRS), Toulouse
- Date Published: February 2015
- availability: Available
- format: Paperback
- isbn: 9781107630697
£
43.99
Paperback
Other available formats:
Hardback, eBook
Looking for an inspection copy?
This title is not currently available on inspection
-
This is the first comprehensive introduction to the powerful moment approach for solving global optimization problems (and some related problems) described by polynomials (and even semi-algebraic functions). In particular, the author explains how to use relatively recent results from real algebraic geometry to provide a systematic numerical scheme for computing the optimal value and global minimizers. Indeed, among other things, powerful positivity certificates from real algebraic geometry allow one to define an appropriate hierarchy of semidefinite (SOS) relaxations or LP relaxations whose optimal values converge to the global minimum. Several extensions to related optimization problems are also described. Graduate students, engineers and researchers entering the field can use this book to understand, experiment with and master this new approach through the simple worked examples provided.
Read more- The first textbook entirely devoted to this hot topic in optimization and computer science
- Demonstrates the power and versatility of the new moment approach
- Introduces new powerful algebraic techniques that have potential uses in many other fields and applications
Reviews & endorsements
'This monograph may be considered as a comprehensive introduction to solving global optimization problems described by polynomials and even semi-algebraic functions. The book is accompanied by a MATLAB® freeware software that implements the described methodology … The well written and extensive introduction may help the reader to knowingly use the book.' Jerzy Ombach, Zentralblatt MATH
See more reviews'This book provides an accessible introduction to very recent developments in the field of polynomial optimisation, i.e., the task of finding the infimum of a polynomial function on a set defined by polynomial constraints … Every chapter contains additional exercises and a guide to the (free) Matlab software GloptiPoly. Therefore, this really well-written book provides an ideal introduction for individual learning and is well suited as the basis for a course on polynomical optimisation. Cordian Riener, Mathematical Reviews
Customer reviews
Not yet reviewed
Be the first to review
Review was not posted due to profanity
×Product details
- Date Published: February 2015
- format: Paperback
- isbn: 9781107630697
- length: 354 pages
- dimensions: 229 x 152 x 19 mm
- weight: 0.5kg
- contains: 15 b/w illus. 2 colour illus.
- availability: Available
Table of Contents
Preface
List of symbols
1. Introduction and messages of the book
Part I. Positive Polynomials and Moment Problems:
2. Positive polynomials and moment problems
3. Another look at nonnegativity
4. The cone of polynomials nonnegative on K
Part II. Polynomial and Semi-algebraic Optimization:
5. The primal and dual points of view
6. Semidefinite relaxations for polynomial optimization
7. Global optimality certificates
8. Exploiting sparsity or symmetry
9. LP relaxations for polynomial optimization
10. Minimization of rational functions
11. Semidefinite relaxations for semi-algebraic optimization
12. An eigenvalue problem
Part III. Specializations and Extensions:
13. Convexity in polynomial optimization
14. Parametric optimization
15. Convex underestimators of polynomials
16. Inverse polynomial optimization
17. Approximation of sets defined with quantifiers
18. Level sets and a generalization of the Löwner-John's problem
Appendix A. Semidefinite programming
Appendix B. The GloptiPoly software
References
Index.-
General Resources
Find resources associated with this title
Type Name Unlocked * Format Size Showing of
This title is supported by one or more locked resources. Access to locked resources is granted exclusively by Cambridge University Press to lecturers whose faculty status has been verified. To gain access to locked resources, lecturers should sign in to or register for a Cambridge user account.
Please use locked resources responsibly and exercise your professional discretion when choosing how you share these materials with your students. Other lecturers may wish to use locked resources for assessment purposes and their usefulness is undermined when the source files (for example, solution manuals or test banks) are shared online or via social networks.
Supplementary resources are subject to copyright. Lecturers are permitted to view, print or download these resources for use in their teaching, but may not change them or use them for commercial gain.
If you are having problems accessing these resources please contact [email protected].
Sorry, this resource is locked
Please register or sign in to request access. If you are having problems accessing these resources please email [email protected]
Register Sign in» Proceed
You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.
Continue ×Are you sure you want to delete your account?
This cannot be undone.
Thank you for your feedback which will help us improve our service.
If you requested a response, we will make sure to get back to you shortly.
×