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SpringerBriefs in Mathematics

Optimization of Polynomials in Non-Commuting Variables

Authors: Burgdorf, Sabine, Klep, Igor, Povh, Janez

  • 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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eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-33338-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA
  • ISBN 978-3-319-33336-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

Table of contents (5 chapters)

  • Selected Results from Algebra and Mathematical Optimization

    Burgdorf, Sabine (et al.)

    Pages 1-34

  • Detecting Sums of Hermitian Squares

    Burgdorf, Sabine (et al.)

    Pages 35-44

  • Cyclic Equivalence to Sums of Hermitian Squares

    Burgdorf, Sabine (et al.)

    Pages 45-62

  • Eigenvalue Optimization of Polynomials in Non-commuting Variables

    Burgdorf, Sabine (et al.)

    Pages 63-85

  • Trace Optimization of Polynomials in Non-commuting Variables

    Burgdorf, Sabine (et al.)

    Pages 87-99

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-33338-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA
  • ISBN 978-3-319-33336-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Optimization of Polynomials in Non-Commuting Variables
Authors
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 and Tables
2 illustrations in colour
Topics