Moment-sos Hierarchy, The: Lectures In Probability, Statistics, Computational Geometry, Control And Nonlinear Pdes
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A01=Didier Henrion
A01=Jean Bernard Lasserre
A01=Milan Korda
Author_Didier Henrion
Author_Jean Bernard Lasserre
Author_Milan Korda
Category=PBU
Convex Relaxation
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Generalized Moment Problem (GMP)
Lebesgue Decomposition
Moment-SOS Hierarchy
Nonlinear Partial Differential Equations
Optimal Control
Optimal Design
Polynomial Optimization Problems
Semidefinite Program
Product details
- ISBN 9781786348531
- Publication Date: 17 Nov 2020
- Publisher: World Scientific Europe Ltd
- Publication City/Country: GB
- Product Form: Hardback
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The Moment-SOS hierarchy is a powerful methodology that is used to solve the Generalized Moment Problem (GMP) where the list of applications in various areas of Science and Engineering is almost endless. Initially designed for solving polynomial optimization problems (the simplest example of the GMP), it applies to solving any instance of the GMP whose description only involves semi-algebraic functions and sets. It consists of solving a sequence (a hierarchy) of convex relaxations of the initial problem, and each convex relaxation is a semidefinite program whose size increases in the hierarchy.The goal of this book is to describe in a unified and detailed manner how this methodology applies to solving various problems in different areas ranging from Optimization, Probability, Statistics, Signal Processing, Computational Geometry, Control, Optimal Control and Analysis of a certain class of nonlinear PDEs. For each application, this unconventional methodology differs from traditional approaches and provides an unusual viewpoint. Each chapter is devoted to a particular application, where the methodology is thoroughly described and illustrated on some appropriate examples.The exposition is kept at an appropriate level of detail to aid the different levels of readers not necessarily familiar with these tools, to better know and understand this methodology.
