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＜電子ブック＞
Optimization of Polynomials in Non-Commuting Variables / by Sabine Burgdorf, Igor Klep, Janez Povh
(SpringerBriefs in Mathematics. ISSN:21918201)

版	1st ed. 2016.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2016
本文言語	英語
大きさ	XV, 104 p. 2 illus. in color : online resource
著者標目	*Burgdorf, Sabine author Klep, Igor author Povh, Janez author SpringerLink (Online service)
件　名	LCSH:Algebraic geometry LCSH:Quantum computers LCSH:Operations research LCSH:Management science LCSH:Computer software LCSH:System theory LCSH:Control theory FREE:Algebraic Geometry FREE:Quantum Computing FREE:Operations Research, Management Science FREE:Mathematical Software FREE:Systems Theory, Control
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-319-33338-0

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