MARC details
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07620cam a2200805 a 4500 |
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ocn624365972 |
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OCoLC |
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20220713030747.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS--GENERAL INFORMATION |
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m o d |
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cr cuu|||uu||| |
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100520s2010 enka ob 001 0 eng d |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
LLB |
| Language of cataloging |
eng |
| Description conventions |
pn |
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LLB |
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N$T |
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OCLCQ |
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CDX |
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OCLCQ |
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YDXCP |
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OCLCF |
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OCLCO |
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OCLCQ |
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AGLDB |
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OCLCQ |
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VTS |
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VT2 |
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OCLCQ |
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WYU |
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OCLCO |
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STF |
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OCLCO |
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JBG |
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LEAUB |
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M8D |
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AJS |
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OCLCO |
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OCLCQ |
| 016 7# - NATIONAL BIBLIOGRAPHIC AGENCY CONTROL NUMBER |
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| Record control number |
015369161 |
| Source |
Uk |
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666256886 |
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670430586 |
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1055403219 |
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1063812033 |
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1086435527 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781848164468 |
| Qualifying information |
(electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
1848164467 |
| Qualifying information |
(electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9786612760006 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
6612760001 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| Cancelled/invalid ISBN |
1848164459 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| Cancelled/invalid ISBN |
9781848164451 |
| 024 8# - OTHER STANDARD IDENTIFIER |
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| Standard number or code |
9786612760006 |
| 029 1# - (OCLC) |
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| OCLC library identifier |
AU@ |
| System control number |
000051395989 |
| 029 1# - (OCLC) |
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| OCLC library identifier |
DEBBG |
| System control number |
BV043138384 |
| 029 1# - (OCLC) |
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| OCLC library identifier |
DEBSZ |
| System control number |
421675705 |
| 029 1# - (OCLC) |
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| OCLC library identifier |
GBVCP |
| System control number |
803174098 |
| 035 ## - SYSTEM CONTROL NUMBER |
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| System control number |
(OCoLC)624365972 |
| Canceled/invalid control number |
(OCoLC)666256886 |
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(OCoLC)670430586 |
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(OCoLC)1055403219 |
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(OCoLC)1063812033 |
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(OCoLC)1086435527 |
| 037 ## - SOURCE OF ACQUISITION |
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| Stock number |
276000 |
| Source of stock number/acquisition |
MIL |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA402.5 |
| Item number |
.L37 2010eb |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
MAT |
| Subject category code subdivision |
042000 |
| Source |
bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
519.6 |
| Edition number |
22 |
| 049 ## - LOCAL HOLDINGS (OCLC) |
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| Holding library |
MAIN |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Lasserre, Jean-Bernard, |
| Dates associated with a name |
1953- |
| 9 (RLIN) |
381471 |
| 245 10 - TITLE STATEMENT |
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| Title |
Moments, positive polynomials and their applications / |
| Statement of responsibility, etc |
Jean Bernard Lasserre. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Place of publication, distribution, etc |
London : |
| Name of publisher, distributor, etc |
Imperial College Press ; |
| Place of publication, distribution, etc |
Singapore : |
| Name of publisher, distributor, etc |
Distributed by World Scientific Pub. Co., |
| Date of publication, distribution, etc |
©2010. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
1 online resource (xxi, 361 pages) : |
| Other physical details |
illustrations (some color). |
| 336 ## - |
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text |
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txt |
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rdacontent |
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computer |
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c |
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rdamedia |
| 338 ## - |
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online resource |
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cr |
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rdacarrier |
| 490 1# - SERIES STATEMENT |
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| Series statement |
Imperial College Press optimization series, |
| International Standard Serial Number |
2041-1677 ; |
| Volume number/sequential designation |
v. 1 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references (pages 341-358) and index. |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
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-definite 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. Semidefinite 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 -- 5. Global optimization over polynomials. 5.1. The primal and dual perspectives. 5.2. Unconstrained polynomial optimization. 5.3. Constrained polynomial optimization : semidefinite 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 unified 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. Semidefinite 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. Semidefinite 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. 12.4. Summary. 12.5. Exercises. 12.6. Notes and sources -- 13. Min-max problems and Nash equilibria. 13.1. Robust polynomial optimization. 13.2. Minimizing the sup of finitely many rational cunctions. 13.3. Application to Nash equilibria. 13.4. Exercises. 13.5. Notes and sources -- 14. Bounds on linear PDE. 14.1. Linear partial differential equations. 14.2. Notes and sources. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
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. |
| 588 0# - |
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Print version record. |
| 590 ## - LOCAL NOTE (RLIN) |
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| Local note |
eBooks on EBSCOhost |
| Provenance (VM) [OBSOLETE] |
EBSCO eBook Subscription Academic Collection - Worldwide |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Mathematical optimization. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Moment problems (Mathematics) |
| 9 (RLIN) |
226483 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Geometry, Algebraic. |
| 9 (RLIN) |
101299 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Polynomials. |
| 9 (RLIN) |
128196 |
| 650 #6 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Optimisation mathématique. |
| 9 (RLIN) |
878326 |
| 650 #6 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Problèmes des moments (Mathématiques) |
| 9 (RLIN) |
1463471 |
| 650 #6 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Géométrie algébrique. |
| 9 (RLIN) |
894815 |
| 650 #6 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Polynômes. |
| 9 (RLIN) |
951770 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
MATHEMATICS |
| General subdivision |
Optimization. |
| Source of heading or term |
bisacsh |
| 9 (RLIN) |
924403 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Geometry, Algebraic. |
| Source of heading or term |
fast |
| -- |
(OCoLC)fst00940902 |
| 9 (RLIN) |
101299 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Mathematical optimization. |
| Source of heading or term |
fast |
| -- |
(OCoLC)fst01012099 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Moment problems (Mathematics) |
| Source of heading or term |
fast |
| -- |
(OCoLC)fst01025012 |
| 9 (RLIN) |
226483 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Polynomials. |
| Source of heading or term |
fast |
| -- |
(OCoLC)fst01070715 |
| 9 (RLIN) |
128196 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Positives Polynom |
| Source of heading or term |
gnd |
| 9 (RLIN) |
1463472 |
| 655 #0 - INDEX TERM--GENRE/FORM |
|---|
| Genre/form data or focus term |
Electronic book. |
| 655 #4 - INDEX TERM--GENRE/FORM |
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| Genre/form data or focus term |
Electronic book. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
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| Corporate name or jurisdiction name as entry element |
World Scientific (Firm) |
| 9 (RLIN) |
74845 |
| 776 1# - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| International Standard Book Number |
1848164459 |
| 776 1# - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| International Standard Book Number |
9781848164451 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
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| Uniform title |
Imperial College Press optimization series ; |
| Volume number/sequential designation |
v. 1. |
| 9 (RLIN) |
340731 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
<a href="https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=340588">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=340588</a> |
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Coutts Information Services |
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COUT |
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15220667 |
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EBSCOhost |
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EBSC |
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340588 |
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YBP Library Services |
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YANK |
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3511269 |
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92 |
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INOPJ |
