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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| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
London
Imperial College Press
c2010
|
| Schriftenreihe: | Imperial College Press optimization series
v. 1 |
| Schlagwörter: | |
| Links: | http://www.worldscientific.com/worldscibooks/10.1142/P665#t=toc http://www.worldscientific.com/worldscibooks/10.1142/P665#t=toc |
| Zusammenfassung: | 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 |
| Umfang: | xxi, 361 p. ill. (some col.) |
| ISBN: | 9781848164468 |
Internformat
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Datensatz im Suchindex
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| author | Lasserre, Jean-Bernard 1953- |
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| dewey-full | 519.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.6 |
| dewey-search | 519.6 |
| dewey-sort | 3519.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV044633431 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T18:07:33Z |
| institution | BVB |
| isbn | 9781848164468 |
| language | English |
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| physical | xxi, 361 p. ill. (some col.) |
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| publishDate | 2010 |
| publishDateSearch | 2010 |
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| publisher | Imperial College Press |
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| series2 | Imperial College Press optimization series |
| spelling | Lasserre, Jean-Bernard 1953- Verfasser (DE-588)121290255 aut Moments, positive polynomials and their applications Jean Bernard Lasserre London Imperial College Press c2010 xxi, 361 p. ill. (some col.) txt rdacontent c rdamedia cr rdacarrier Imperial College Press optimization series v. 1 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 Mathematical optimization Moment problems (Mathematics) Geometry, Algebraic Polynomials Positives Polynom (DE-588)4193849-5 gnd rswk-swf Positives Polynom (DE-588)4193849-5 s 1\p DE-604 Erscheint auch als Druck-Ausgabe 1848164459 Erscheint auch als Druck-Ausgabe 9781848164451 http://www.worldscientific.com/worldscibooks/10.1142/P665#t=toc Verlag URL des Erstveroeffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lasserre, Jean-Bernard 1953- Moments, positive polynomials and their applications Mathematical optimization Moment problems (Mathematics) Geometry, Algebraic Polynomials Positives Polynom (DE-588)4193849-5 gnd |
| subject_GND | (DE-588)4193849-5 |
| title | Moments, positive polynomials and their applications |
| title_auth | Moments, positive polynomials and their applications |
| title_exact_search | Moments, positive polynomials and their applications |
| title_full | Moments, positive polynomials and their applications Jean Bernard Lasserre |
| title_fullStr | Moments, positive polynomials and their applications Jean Bernard Lasserre |
| title_full_unstemmed | Moments, positive polynomials and their applications Jean Bernard Lasserre |
| title_short | Moments, positive polynomials and their applications |
| title_sort | moments positive polynomials and their applications |
| topic | Mathematical optimization Moment problems (Mathematics) Geometry, Algebraic Polynomials Positives Polynom (DE-588)4193849-5 gnd |
| topic_facet | Mathematical optimization Moment problems (Mathematics) Geometry, Algebraic Polynomials Positives Polynom |
| url | http://www.worldscientific.com/worldscibooks/10.1142/P665#t=toc |
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