Moments, Positive Polynomials And Their Applications (Hardcover)

Many important problems 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, in a unified manual, 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 of this invaluable volume, the methodology is particularized and described in detail for various applications, including global optimization, probability, optimal context, mathematical finance, multivariate integration, etc., and examples are provided for each particular application.

General

Imprint:	Imperial College Press
Country of origin:	United Kingdom
Series:	Series On Optimization And Its Applications, 1
Release date:	October 2009
First published:	October 2009
Authors:	Jean-Bernard Lasserre
Dimensions:	235 x 155 x 25mm (L x W x T)
Format:	Hardcover
Pages:	384
ISBN-13:	978-1-84816-445-1
Categories:	Books > Science & Mathematics > Mathematics > Optimization > General
LSN:	1-84816-445-9
Barcode:	9781848164451

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