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An introduction to polynomial and semi-algebraic optimization

Author: Jean-Bernard Lasserre
Publisher: New York : Cambridge University Press, 2015.
Series: Cambridge texts in applied mathematics, no. 52.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Lasserre, Jean-Bernard, 1953-
Introduction to polynomial and semi-algebraic optimization.
Cambridge : Cambridge University Press, 2015
(DLC) 2014031786
(OCoLC)886382380
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Jean-Bernard Lasserre
ISBN: 9781107447226 1107447224 9781107060579 1107060575 9781107630697 110763069X
OCLC Number: 903198925
Language Note: English.
Description: 1 online resource.
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.
Series Title: Cambridge texts in applied mathematics, no. 52.
Responsibility: Jean Bernard Lasserre, LAAS-CNRS and Institut de mathématiques, Toulouse, France.

Abstract:

This is the first comprehensive introduction to the powerful moment approach for solving global optimization problems. Graduate students, engineers and researchers entering the field can use this  Read more...

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'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 Read more...

 
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