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Moments, positive polynomials and th...

Lasserre, Jean Bernard, (1953-)

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Moments, positive polynomials and their applications /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Moments, positive polynomials and their applications // Jean Bernard Lasserre.
作者:	Lasserre, Jean Bernard,
出版者:	London :Imperial College Press ; : c2010.,
面頁冊數:	xxi, 361 p. :ill. ;24 cm.
標題:	Mathematical optimization. -
ISBN:	9781848164451 (hbk.) :

Moments, positive polynomials and their applications /
Lasserre, Jean Bernard,1953-

Moments, positive polynomials and their applications /Jean Bernard Lasserre. - London :Imperial College Press ;c2010. - xxi, 361 p. :ill. ;24 cm. - Imperial College Press optimization series,v. 12041-1677 ;.

Includes bibliographical references (p. 341-358) and index.

"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." -- Book cover

ISBN: 9781848164451 (hbk.) :US96.00Subjects--Topical Terms:

517763
Mathematical optimization.

LC Class. No.: QA402.5 / .L365 2010

Dewey Class. No.: 519.6

Moments, positive polynomials and their applications /
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020 $a 9781848164451 (hbk.) : $c US96.00
020 $a 1848164459 (hbk.)
035 $a AS-BW-101-N-05
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050 0 0 $a QA402.5 $b .L365 2010
082 0 0 $a 519.6 $2 23
100 1 $a Lasserre, Jean Bernard, $d 1953- $3 1536481
245 1 0 $a Moments, positive polynomials and their applications / $c Jean Bernard Lasserre.
260 # $a London : $a Signapore ; $b Imperial College Press ; $a Hackensack, NJ : $c c2010. $b Distributed by World Scientific Publishing Co.,
300 $a xxi, 361 p. : $b ill. ; $c 24 cm.
490 1 0 $a Imperial College Press optimization series, $x 2041-1677 ; $v v. 1
504 $a Includes bibliographical references (p. 341-358) and index.
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, 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." -- Book cover
650 # 0 $a Mathematical optimization. $3 517763
650 # 0 $a Moment problems (Mathematics) $3 706589
650 # 0 $a Geometry, Algebraic. $3 532048
650 # 0 $a Polynomials. $3 604754