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Optimization of polynomials in non-commuting variables

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Optimization of polynomials in non-commuting variables/ by Sabine Burgdorf, Igor Klep, Janez Povh.
Author:	Burgdorf, Sabine.
other author:	Klep, Igor.
Published:	Cham :Springer International Publishing : : 2016.,
Description:	xv, 104 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Mathematical optimization. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-33338-0
ISBN:	9783319333380

Optimization of polynomials in non-commuting variables
Burgdorf, Sabine.

Optimization of polynomials in non-commuting variables[electronic resource] /by Sabine Burgdorf, Igor Klep, Janez Povh. - Cham :Springer International Publishing :2016. - xv, 104 p. :ill., digital ;24 cm. - SpringerBriefs in mathematics,2191-8198. - SpringerBriefs in mathematics..

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.

ISBN: 9783319333380

Standard No.: 10.1007/978-3-319-33338-0doiSubjects--Topical Terms:

527675
Mathematical optimization.

LC Class. No.: QA402.5

Dewey Class. No.: 519.6

Optimization of polynomials in non-commuting variables
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520 $a 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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