An introduction to polynomial and semi-algebraic optimization / Jean Bernard Lasserre, LAAS-CNRS and Institut de Mathématiques, Toulouse, France.
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...
| Uniform Title: | Cambridge texts in applied mathematics ;
52. |
|---|---|
| Main Author: | |
| Language: | English |
| Published: |
Cambridge :
Cambridge University Press,
2015.
|
| Series: | Cambridge texts in applied mathematics ;
52. |
| Subjects: | |
| Online Access: | |
| Physical Description: | 1 online resource (xiv, 339 pages) : digital, PDF file(s). |
| Variant Title: |
An Introduction to Polynomial & Semi-Algebraic Optimization. |
| Format: | Electronic eBook |
Contents:
- Machine generated contents note: 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 Lowner-John's problem; Appendix A. Semidefinite programming; Appendix B. The GloptiPoly software; Bibliography; Index.