Moments, Positive Polynomials And Their Applications
Author:   Jean Bernard Lasserre (Laas-cnrs & Inst Of Mathematics, Univ Of Toulouse, France)
Publisher:   Imperial College Press
Volume:   1
ISBN:  

9781848164451


Pages:   384
Publication Date:   02 October 2009
Format:   Hardback
Availability:   In Print   Availability explained
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Moments, Positive Polynomials And Their Applications


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Overview

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.

Full Product Details

Author:   Jean Bernard Lasserre (Laas-cnrs & Inst Of Mathematics, Univ Of Toulouse, France)
Publisher:   Imperial College Press
Imprint:   Imperial College Press
Volume:   1
Dimensions:   Width: 15.50cm , Height: 2.30cm , Length: 23.10cm
Weight:   0.703kg
ISBN:  

9781848164451


ISBN 10:   1848164459
Pages:   384
Publication Date:   02 October 2009
Audience:   College/higher education ,  Professional and scholarly ,  Tertiary & Higher Education ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print   Availability explained
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

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.

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