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An introduction to polynomial and semi-algebraic optimization Jean Bernard Lasserre, LAAS-CNRS and Institut de Mathematiques, Toulouse, France

By: Series: Cambridge texts in applied mathematicsDescription: xiv, 339 p. ill. ; 24 cmISBN:
  • 9781107060579 (hardback)
  • 1107060575 (hardback)
  • 9781107630697 (paperback)
  • 110763069X (paperback)
Subject(s): DDC classification:
  • 512.9422
LOC classification:
  • QA161.P59
Other classification:
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.
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Holdings
Item type Current library Call number Copy number Status Date due Barcode
Carti IMAR 512.9422-LAS (Browse shelf(Opens below)) 1 Available 0035803

eng

Bibliografie p. 324
Index p. 327

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.

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