ENGLISH

Optimization of Polynomials in Non-Commuting Variables

By Sabine Burgdorf , Igor Klep , Janez Povh (auth.)

Book information

Publisher
Springer International Publishing
Year
2016
ISBN
978-3-319-33336-6, 978-3-319-33338-0
DOI
10.1007/978-3-319-33338-0
Language
english
Format
PDF
Filesize
1 MB (1526738 bytes)
Series
SpringerBriefs in Mathematics
Edition
1
Pages
XV, 104\118
Time added
2016-07-20 04:00:00
Algebraic Geometry; Quantum Computing; OperationsControlManagement Science; Mathematical Software; Systems

Description

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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