Jean Bernard Lasserre ICP Moments, Positive Polynomials and Their Applications Lasserre Imperial College Press www.icpress.co.uk Imperial College Press ICP 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. Moments, Positive Polynomials and Their Applications P665 hc ,!7IB8E8-bgeefb! ISBN-13 978-1-84816-445-1 ISBN-10 1-84816-445-9 Moments, Positive Polynomials and Their Applications Imperial College Press Optimization Series Vol. 1 Vol. 1 Imperial College Press Optimization Series Vol. 1
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Jean Bernard Lasserre
ICPMom
ents, Positive Polynomials
and Their A
pplicationsLasserre
Imperial College Presswww.icpress.co.uk
Imperial College PressICP
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.
Moments, Positive Polynomials and Their Applications
P665 hc
,!7IB8E8-bgeefb!ISBN-13 978-1-84816-445-1ISBN-10 1-84816-445-9
Moments, Positive Polynomials and
Their Applications
Imperial College Press Optimization Series Vol. 1Vol. 1
Imperial College Press Optimization Series Vol. 1
Related Documents
