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Moments, Positive Polynomials And Their Applications.
Many important applications in global optimization, algebra, probability and statistics, applied mathematics, control theory, financial mathematics, inverse problems, etc. can be modeled as a particular instance of the Generalized Moment Problem (GMP) . This book introduces a new general methodology...
| Clasificación: | Libro Electrónico |
|---|---|
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
World Scientific
2009.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000M 4500 | ||
|---|---|---|---|
| 001 | EBOOKCENTRAL_ocn729020365 | ||
| 003 | OCoLC | ||
| 005 | 20240329122006.0 | ||
| 006 | m o d | ||
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| 008 | 101115s2009 xx o 000 0 eng d | ||
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| 020 | |a 1282760009 | ||
| 020 | |a 9781282760004 | ||
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| 049 | |a UAMI | ||
| 245 | 0 | 0 | |a Moments, Positive Polynomials And Their Applications. |
| 260 | |b World Scientific |c 2009. | ||
| 300 | |a 1 online resource (384) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 505 | 0 | |a Cover13; -- Contents -- Preface -- Acknowledgments -- Part I Moments and Positive Polynomials -- 1. The Generalized Moment Problem -- 1.1 Formulations -- 1.2 Duality Theory -- 1.3 Computational Complexity -- 1.4 Summary -- 1.5 Exercises -- 1.6 Notes and Sources -- 2. Positive Polynomials -- 2.1 Sum of Squares Representations and Semi-de nite Optimization -- 2.2 Nonnegative Versus s.o.s. Polynomials -- 2.3 Representation Theorems: Univariate Case -- 2.4 Representation Theorems: Mutivariate Case -- 2.5 Polynomials Positive on a Compact Basic Semi-algebraic Set -- 2.6 Polynomials Nonnegative on Real Varieties -- 2.7 Representations with Sparsity Properties -- 2.8 Representation of Convex Polynomials -- 2.9 Summary -- 2.10 Exercises -- 2.11 Notes and Sources -- 3. Moments -- 3.1 The One-dimensional Moment Problem -- 3.2 The Multi-dimensional Moment Problem -- 3.3 The K-moment Problem -- 3.4 Moment Conditions for Bounded Density -- 3.5 Summary -- 3.6 Exercises -- 3.7 Notes and Sources -- 4. Algorithms for Moment Problems -- 4.1 The Overall Approach -- 4.2 Semide nite Relaxations -- 4.3 Extraction of Solutions -- 4.4 Linear Relaxations -- 4.5 Extensions -- 4.6 Exploiting Sparsity -- 4.7 Summary -- 4.8 Exercises -- 4.9 Notes and Sources -- 4.10 Proofs -- Part II Applications -- 5. Global Optimization over Polynomials -- 5.1 The Primal and Dual Perspectives -- 5.2 Unconstrained Polynomial Optimization -- 5.3 Constrained Polynomial Optimization: Semide nite Relaxations -- 5.4 Linear Programming Relaxations -- 5.5 Global Optimality Conditions -- 5.6 Convex Polynomial Programs -- 5.7 Discrete Optimization -- 5.8 Global Minimization of a Rational Function -- 5.9 Exploiting Symmetry -- 5.10 Summary -- 5.11 Exercises -- 5.12 Notes and Sources -- 6. Systems of Polynomial Equations -- 6.1 Introduction -- 6.2 Finding a Real Solution to Systems of Polynomial Equations -- 6.3 Finding All Complex and/or All Real Solutions: A Uni ed Treatment -- 6.4 Summary -- 6.5 Exercises -- 6.6 Notes and Sources -- 7. Applications in Probability -- 7.1 Upper Bounds on Measures with Moment Conditions -- 7.2 Measuring Basic Semi-algebraic Sets -- 7.3 Measures with Given Marginals -- 7.4 Summary -- 7.5 Exercises -- 7.6 Notes and Sources -- 8. Markov Chains Applications -- 8.1 Bounds on Invariant Measures -- 8.2 Evaluation of Ergodic Criteria -- 8.3 Summary -- 8.4 Exercises -- 8.5 Notes and Sources -- 9. Application in Mathematical Finance -- 9.1 Option Pricing with Moment Information -- 9.2 Option Pricing with a Dynamic Model -- 9.3 Summary -- 9.4 Notes and Sources -- 10. Application in Control -- 10.1 Introduction -- 10.2 Weak Formulation of Optimal Control Problems -- 10.3 Semide finite Relaxations for the OCP -- 10.4 Summary -- 10.5 Notes and Sources -- 11. Convex Envelope and Representation of Convex Sets -- 11.1 The Convex Envelope of a Rational Function -- 11.2 Semide finite Representation of Convex Sets -- 11.3 Algebraic Certificates of Convexity -- 11.4 Summary -- 11.5 Exercises -- 11.6 Notes and Sources -- 12. Multivariate Integration -- 12.1 Integration of a Rational Function -- 12.2 Integration of Exponentials of Polynomials -- 12.3 Maximum Entropy Estimation. | |
| 520 | |a Many important applications in global optimization, algebra, probability and statistics, applied mathematics, control theory, financial mathematics, inverse problems, etc. can be modeled as a particular instance of the Generalized Moment Problem (GMP) . This book introduces a new general methodology to solve the GMP when its data are polynomials and basic semi-algebraic sets. This methodology combines semidefinite programming with recent results from real algebraic geometry to provide a hierarchy of semidefinite relaxations converging to the desired optimal value. Applied on appropriate cones. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Moments method (Statistics) | |
| 650 | 0 | |a Polynomials. | |
| 650 | 6 | |a Méthodes des moments (Statistique) | |
| 650 | 6 | |a Polynômes. | |
| 650 | 7 | |a Moments method (Statistics) |2 fast | |
| 650 | 7 | |a Polynomials |2 fast | |
| 655 | 4 | |a Electronic resource. | |
| 720 | |a Lasserre Jean Bernard. | ||
| 758 | |i has work: |a Moments, positive polynomials and their applications (Work) |1 https://id.oclc.org/worldcat/entity/E39PCFDfkMwHTJgG7rtjWWQH4q |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=1679371 |z Texto completo |
| 938 | |a EBL - Ebook Library |b EBLB |n EBL1679371 | ||
| 938 | |a ProQuest MyiLibrary Digital eBook Collection |b IDEB |n 276000 | ||
| 994 | |a 92 |b IZTAP | ||