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...
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
London : Singapore :
Imperial College Press ; Distributed by World Scientific Pub. Co.,
©2010.
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| Series: | Imperial College Press optimization series ;
v. 1. |
| Subjects: | |
| Online Access: | CONNECT |
| Summary: | 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, standard duality in convex optimization nicely expresses the duality between moments and positive polynomials. In the second part, the methodology is particularized and described in detail for various applications, including global optimization, probability, optimal control, mathematical finance, multivariate integration, etc., and examples are provided for each particular application. |
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| Item Description: | EBSCO eBook Academic Comprehensive Collection North America |
| Physical Description: | 1 online resource (xxi, 361 pages) : illustrations (some color). |
| Bibliography: | Includes bibliographical references (pages 341-358) and index. |
| ISBN: | 9781848164468 1848164467 9786612760006 6612760001 |
| ISSN: | 2041-1677 ; |
