Optimization of Polynomials in Non-Commuting Variables (SpringerBriefs in Mathematics) - Softcover

Burgdorf, Sabine; Klep, Igor; Povh, Janez

 
9783319333366: Optimization of Polynomials in Non-Commuting Variables (SpringerBriefs in Mathematics)
Softcover
ISBN 10: 3319333364 ISBN 13: 9783319333366
Verlag: Springer, 2016

Inhaltsangabe

This book presents recent results on positivity and optimization of polynomials in non-commuting variables. Researchers in non-commutative algebraic geometry, control theory, system engineering, optimization, quantum physics and information science will find the unified notation and mixture of algebraic geometry and mathematical programming useful. Theoretical results are matched with algorithmic considerations; several examples and information on how to use NCSOStools open source package to obtain the results provided. Results are presented on detecting the eigenvalue and trace positivity of polynomials in non-commuting variables using Newton chip method and Newton cyclic chip method, relaxations for constrained and unconstrained optimization problems, semidefinite programming formulations of the relaxations and finite convergence of the hierarchies of these relaxations, and the practical efficiency of algorithms.

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Críticas

“The book covers the basics of NC polynomial optimization, building on elementary material from algebra and analysis as well as on more advanced concepts such as the Gelfand-Naimark-Segal construction. ... This short yet very accessible book written by three leading experts in the field contains many examples, including explicit reproducible computations with their open source Mat lab toolbox NCSOS tools. It can be recommended to young researchers with an interest in polynomial optimization.” (Didier Henrion, Mathematical Reviews, May, 2017)

Reseña del editor

This book presents recent results on positivity and optimization of polynomials in non-commuting variables. Researchers in non-commutative algebraic geometry, control theory, system engineering, optimization, quantum physics and information science will find the unified notation and mixture of algebraic geometry and mathematical programming useful. Theoretical results are matched with algorithmic considerations; several examples and information on how to use NCSOStools open source package to obtain the results provided. Results are presented on detecting the eigenvalue and trace positivity of polynomials in non-commuting variables using Newton chip method and Newton cyclic chip method, relaxations for constrained and unconstrained optimization problems, semidefinite programming formulations of the relaxations and finite convergence of the hierarchies of these relaxations, and the practical efficiency of algorithms.

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Verlag
Springer
Erscheinungsdatum
2016
Sprache
Englisch
ISBN 10 
3319333364
ISBN 13 
9783319333366
Einband
Tapa blanda
Auflage
1
Anzahl der Seiten
120
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
CMN Printpool Inh. Mathis Neumann
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Hamburg
Deutschland

Weitere beliebte Ausgaben desselben Titels

9783319333373: Optimization of Polynomials in Non-Commuting Variables

Vorgestellte Ausgabe

ISBN 10:  3319333372 ISBN 13:  9783319333373
Verlag: Springer, 2016
Softcover