大葉大學圖書館 |

Optimization of polynomials in non-commuting variables[electronic resource] /

紀錄類型:	書目-電子資源 : Monograph/item
杜威分類號:	519.6
書名/作者:	Optimization of polynomials in non-commuting variables/ by Sabine Burgdorf, Igor Klep, Janez Povh.
作者:	Burgdorf, Sabine.
其他作者:	Klep, Igor.
出版者:	Cham : : Springer International Publishing :, 2016.
面頁冊數:	xv, 104 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Mathematical optimization.
標題:	Polynomials.
標題:	Variables (Mathematics)
標題:	Mathematics.
標題:	Algebraic Geometry.
標題:	Quantum Computing.
標題:	Operations Research, Management Science.
標題:	Mathematical Software.
標題:	Systems Theory, Control.
ISBN:	9783319333380
ISBN:	9783319333366
摘要、提要註:	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.
電子資源:	http://dx.doi.org/10.1007/978-3-319-33338-0

Optimization of polynomials in non-commuting variables[electronic resource] /
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:

176332
Mathematical optimization.

LC Class. No.: QA402.5

Dewey Class. No.: 519.6

Optimization of polynomials in non-commuting variables[electronic resource] /
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