Positive Polynomials and Sums of Squares
2009
American Mathematical Society (Verlag)
978-0-8218-4402-1 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-4402-1 (ISBN)
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A study of positive polynomials that brings together algebra, geometry and analysis. This book provides an elementary introduction to positive polynomials and sums of squares, the relationship to the moment problem, and the application to polynomial optimization. It is suitable for a student at the beginning graduate level.
The study of positive polynomials brings together algebra, geometry and analysis. The subject is of fundamental importance in real algebraic geometry, when studying the properties of objects defined by polynomial inequalities. Hilbert's 17th problem and its solution in the first half of the 20th century were landmarks in the early days of the subject. More recently, new connections to the moment problem and to polynomial optimization have been discovered. The moment problem relates linear maps on the multidimensional polynomial ring to positive Borel measures.
The study of positive polynomials brings together algebra, geometry and analysis. The subject is of fundamental importance in real algebraic geometry, when studying the properties of objects defined by polynomial inequalities. Hilbert's 17th problem and its solution in the first half of the 20th century were landmarks in the early days of the subject. More recently, new connections to the moment problem and to polynomial optimization have been discovered. The moment problem relates linear maps on the multidimensional polynomial ring to positive Borel measures.
Preliminaries Positive polynomials and sums of square Krivine's Positivstellensatz The moment problem Non-compact case Archimedean $T$-modules Schmudgen's Positivstellensatz Putinar's question Weak isotropy of quadratic forms Scheiderer's local-global principle Semidefinite programming and optimization Appendix 1: Tarski-Seidenberg theorem Appendix 2: Algebraic sets Bibiography.
| Erscheint lt. Verlag | 9.1.2009 |
|---|---|
| Reihe/Serie | Mathematical Surveys and Monographs |
| Zusatzinfo | Illustrations |
| Verlagsort | Providence |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 0-8218-4402-4 / 0821844024 |
| ISBN-13 | 978-0-8218-4402-1 / 9780821844021 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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