An introduction to polynomial and semi-algebraic optimization
Lasserre, Jean-Bernard
An introduction to polynomial and semi-algebraic optimization Jean Bernard Lasserre, LAAS-CNRS and Institut de Mathematiques, Toulouse, France - xiv, 339 p. ill. ; 24 cm - Cambridge texts in applied mathematics .
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.
eng
9781107060579 (hardback) 1107060575 (hardback) 9781107630697 (paperback) 110763069X (paperback)
2014031786
Polynomials
Mathematical optimization
Mathematical Analysis
QA161.P59
512.9422
An introduction to polynomial and semi-algebraic optimization Jean Bernard Lasserre, LAAS-CNRS and Institut de Mathematiques, Toulouse, France - xiv, 339 p. ill. ; 24 cm - Cambridge texts in applied mathematics .
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.
eng
9781107060579 (hardback) 1107060575 (hardback) 9781107630697 (paperback) 110763069X (paperback)
2014031786
Polynomials
Mathematical optimization
Mathematical Analysis
QA161.P59
512.9422