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Optimization of Polynomials in Non-Commuting Variables

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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Series Title
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Call Number
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Publisher
The Author : Springer Cham.,
Collation
-
Language
English
ISBN/ISSN
978-3-319-33338-0
Classification
NONE
Content Type
text
Media Type
computer
Carrier Type
online resource
Edition
-
Subject(s)
Control
Operations Research
Management Science
Algebraic Geometry
Quantum Computing
Mathematical SoSystems Theoryftware
Specific Detail Info
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Statement of Responsibility
Other Information
Cataloger
Yudi
Source
-
Validator
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