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作者 Lasserre, Jean-Bernard, 1953- author
書名 An introduction to polynomial and semi-algebraic optimization / Jean Bernard Lasserre, LAAS-CNRS and Institut de Mathématiques, Toulouse, France
出版項 Cambridge : Cambridge University Press, 2015
國際標準書號 9781107060579
1107060575
9781107630697
110763069X
book jacket
館藏地 索書號 處理狀態 OPAC 訊息 條碼
 數學所圖書室  QA161.P59 L37 2015    在架上    30340200547085
說明 xiv, 339 pages : illustrations ; 23 cm
系列 Cambridge texts in applied mathematics
Cambridge texts in applied mathematics
附註 Includes bibliographical references and index
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 -- 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. Polynomial optimization as 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
主題 Polynomials
Mathematical optimization
Polynomials
Mathematical optimization
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