
Moments, Positive Polynomials And Their Applications
Jean Bernard Lasserre(Author)
Imperial College Press
Published on 2. October 2009
Book
Hardback
384 pages
978-1-84816-445-1 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
London
United Kingdom
Target group
College/higher education
Professional and scholarly
Postgraduates, academics and researchers in mathematical programming, control and optimization.
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 25 mm
Weight
706 gr
ISBN-13
978-1-84816-445-1 (9781848164451)
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Schweitzer Classification
Person
Content
Moments and Positive Polynomials: The Generalized Moment Problem; Nonnegative Polynomials; Moments; Algorithms for Moment Problems; Applications: Optimization over Polynomials; Systems of Polynomial Equations; Applications to Probability and Markov Chains; Application to Mathematical Finance; Applications to Control; Convex Envelope and Representation of Convex Sets; Multivariate Integration; Min-Max Problems and Nash Equilibria; Bounds on Linear PDE.