An introduction to polynomial and semi-algebraic optimization:
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...
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| Main Author: | |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2015
|
| Series: | Cambridge texts in applied mathematics
52 |
| Subjects: | |
| Online Access: | DE-12 DE-92 Volltext |
| 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 other things, powerful positivity certificates from real algebraic geometry allow one to define an appropriate hierarchy of semidefinite (SOS) relaxations or LP relaxations whose optimal values converge to the global minimum. Several extensions to related optimization problems are also described. Graduate students, engineers and researchers entering the field can use this book to understand, experiment with and master this new approach through the simple worked examples provided |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (xiv, 339 pages) |
| ISBN: | 9781107447226 |
| DOI: | 10.1017/CBO9781107447226 |
Staff View
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| 245 | 1 | 0 | |a An introduction to polynomial and semi-algebraic optimization |c Jean Bernard Lasserre, LAAS-CNRS and Institut de Mathématiques, Toulouse, France |
| 246 | 1 | 3 | |a An Introduction to Polynomial & Semi-Algebraic Optimization |
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| 505 | 8 | |a 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 | |
| 520 | |a 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 other things, powerful positivity certificates from real algebraic geometry allow one to define an appropriate hierarchy of semidefinite (SOS) relaxations or LP relaxations whose optimal values converge to the global minimum. Several extensions to related optimization problems are also described. Graduate students, engineers and researchers entering the field can use this book to understand, experiment with and master this new approach through the simple worked examples provided | ||
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Record in the Search Index
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| author | Lasserre, Jean-Bernard 1953- |
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| 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 |
| ctrlnum | (ZDB-20-CBO)CR9781107447226 (OCoLC)992926537 (DE-599)BVBBV043940430 |
| dewey-full | 512.9/422 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9/422 |
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| discipline | Mathematik |
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| id | DE-604.BV043940430 |
| illustrated | Not Illustrated |
| indexdate | 2025-04-23T10:01:08Z |
| institution | BVB |
| isbn | 9781107447226 |
| language | English |
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| oclc_num | 992926537 |
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| physical | 1 online resource (xiv, 339 pages) |
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| spelling | Lasserre, Jean-Bernard 1953- Verfasser (DE-588)121290255 aut An introduction to polynomial and semi-algebraic optimization Jean Bernard Lasserre, LAAS-CNRS and Institut de Mathématiques, Toulouse, France An Introduction to Polynomial & Semi-Algebraic Optimization Cambridge Cambridge University Press 2015 1 online resource (xiv, 339 pages) txt rdacontent c rdamedia cr rdacarrier Cambridge texts in applied mathematics 52 Title from publisher's bibliographic system (viewed on 05 Oct 2015) 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 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 other things, powerful positivity certificates from real algebraic geometry allow one to define an appropriate hierarchy of semidefinite (SOS) relaxations or LP relaxations whose optimal values converge to the global minimum. Several extensions to related optimization problems are also described. Graduate students, engineers and researchers entering the field can use this book to understand, experiment with and master this new approach through the simple worked examples provided Polynomials Mathematical optimization Polynom (DE-588)4046711-9 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Polynom (DE-588)4046711-9 s Optimierung (DE-588)4043664-0 s 1\p DE-604 Erscheint auch als Druckausgabe 978-1-107-06057-9 Erscheint auch als Druckausgabe 978-1-107-63069-7 Cambridge texts in applied mathematics 52 (DE-604)BV046998082 52 https://doi.org/10.1017/CBO9781107447226 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lasserre, Jean-Bernard 1953- An introduction to polynomial and semi-algebraic optimization 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 Polynomials Mathematical optimization Polynom (DE-588)4046711-9 gnd Optimierung (DE-588)4043664-0 gnd Cambridge texts in applied mathematics |
| subject_GND | (DE-588)4046711-9 (DE-588)4043664-0 |
| title | An introduction to polynomial and semi-algebraic optimization |
| title_alt | An Introduction to Polynomial & Semi-Algebraic Optimization |
| title_auth | An introduction to polynomial and semi-algebraic optimization |
| title_exact_search | An introduction to polynomial and semi-algebraic optimization |
| title_full | An introduction to polynomial and semi-algebraic optimization Jean Bernard Lasserre, LAAS-CNRS and Institut de Mathématiques, Toulouse, France |
| title_fullStr | An introduction to polynomial and semi-algebraic optimization Jean Bernard Lasserre, LAAS-CNRS and Institut de Mathématiques, Toulouse, France |
| title_full_unstemmed | An introduction to polynomial and semi-algebraic optimization Jean Bernard Lasserre, LAAS-CNRS and Institut de Mathématiques, Toulouse, France |
| title_short | An introduction to polynomial and semi-algebraic optimization |
| title_sort | an introduction to polynomial and semi algebraic optimization |
| topic | Polynomials Mathematical optimization Polynom (DE-588)4046711-9 gnd Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Polynomials Mathematical optimization Polynom Optimierung |
| url | https://doi.org/10.1017/CBO9781107447226 |
| volume_link | (DE-604)BV046998082 |
| work_keys_str_mv | AT lasserrejeanbernard anintroductiontopolynomialandsemialgebraicoptimization AT lasserrejeanbernard anintroductiontopolynomialsemialgebraicoptimization |