Moment-SOS Hierarchy, The: Lectures in Probability, Statistics, Computational Geometry, Control and Nonlinear PDEs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F20%3A00344924" target="_blank" >RIV/68407700:21230/20:00344924 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1142/q0252" target="_blank" >https://doi.org/10.1142/q0252</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/q0252" target="_blank" >10.1142/q0252</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Moment-SOS Hierarchy, The: Lectures in Probability, Statistics, Computational Geometry, Control and Nonlinear PDEs

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Moment-SOS Hierarchy, The: Lectures in Probability, Statistics, Computational Geometry, Control and Nonlinear PDEs

Popis výsledku anglicky

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.

Druh

B - Odborná kniha

CEP obor

—

OECD FORD obor

20205 - Automation and control systems

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

ISBN

978-1-78634-853-1

Počet stran knihy

248

Název nakladatele

World Scientific

Místo vydání

London

Kód UT WoS knihy

—