Optimization of Polynomials in Non-Commuting Variables
Authors: Burgdorf, Sabine, Klep, Igor, Povh, Janez
Free Preview- Focuses on polynomial optimization problems in matrix unknowns
- Includes fundamental material from algebra, functional analysis and mathematical optimization
- Provides instructions on using NCSOStools open source package to obtain illustrated results
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- About this book
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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.
- Reviews
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“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)
- Table of contents (5 chapters)
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Selected Results from Algebra and Mathematical Optimization
Pages 1-34
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Detecting Sums of Hermitian Squares
Pages 35-44
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Cyclic Equivalence to Sums of Hermitian Squares
Pages 45-62
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Eigenvalue Optimization of Polynomials in Non-commuting Variables
Pages 63-85
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Trace Optimization of Polynomials in Non-commuting Variables
Pages 87-99
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Table of contents (5 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Optimization of Polynomials in Non-Commuting Variables
- Authors
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- Sabine Burgdorf
- Igor Klep
- Janez Povh
- Series Title
- SpringerBriefs in Mathematics
- Copyright
- 2016
- Publisher
- Springer International Publishing
- Copyright Holder
- The Author(s)
- eBook ISBN
- 978-3-319-33338-0
- DOI
- 10.1007/978-3-319-33338-0
- Softcover ISBN
- 978-3-319-33336-6
- Series ISSN
- 2191-8198
- Edition Number
- 1
- Number of Pages
- XV, 104
- Number of Illustrations
- 2 illustrations in colour
- Topics
