Moments, Positive Polynomials And Their Applications (Optimization and Its Applications) - Softcover

Lasserre, Jean Bernard

Softcover

ISBN 10: 1911299735 ISBN 13: 9781911299738

Publisher: Icp, 2009

Synopsis

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.

 

About this title

From the Back Cover

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.

Edition details

• Publisher: Icp
• Publication date: 2009
• Language: English
• ISBN 10: 1911299735
• ISBN 13: 9781911299738
• Binding: Paperback
• Number of pages: 384