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Synopsis
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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Review
“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)
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- PublisherSpringer
- Publication date2016
- ISBN 10 3319333364
- ISBN 13 9783319333366
- BindingPaperback
- LanguageEnglish
- Edition number1
- Number of pages119
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Optimization of Polynomials in Non-commuting Variables
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Optimization of Polynomials in Non-Commuting Variables (SpringerBriefs in Mathematics)
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Optimization of Polynomials in Non-Commuting Variables
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ISBN 10: 3319333364
ISBN 13: 9783319333366
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 120 pp. Englisch. Seller Inventory # 9783319333366
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Optimization of Polynomials in Non-Commuting Variables
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Springer International Publishing, 2016
ISBN 10: 3319333364
ISBN 13: 9783319333366
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Taschenbuch
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Seller Inventory # 9783319333366
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Optimization of Polynomials in Non-commuting Variables
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Optimization of Polynomials in Non-Commuting Variables
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ISBN 13: 9783319333366
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Focuses on polynomial optimization problems in matrix unknownsIncludes fundamental material from algebra, functional analysis and mathematical optimization Provides instructions on using NCSOStools open source package to obtain illustrated . Seller Inventory # 119052224
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Optimization of Polynomials in Non-commuting Variables
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