Optimization of Polynomials in Non-Commuting Variables

Sabine Burgdorf

ISBN 10: 3319333364 / ISBN 13: 9783319333366

Published by Springer International Publishing, Springer International Publishing Jul 2016, 2016

About this Item

Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 120 pp. Englisch.

Seller Inventory # 9783319333366

Bibliographic Details

• Title: Optimization of Polynomials in Non-Commuting Variables
• Publisher: Springer International Publishing, Springer International Publishing Jul 2016
• Publication Date: 2016
• Language: English
• ISBN 10: 3319333364
• ISBN 13: 9783319333366
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 7D millimeters 235 millimeters width by 155 millimeters height by 7 millimeters depth
• Weight: 195 grams

About this title

Synopsis

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.

Review

“The book covers the basics of NC polynomial optimization, building on elementary material from algebra and analysis as well as on more advanced concepts such as the Gelfand-Naimark-Segal construction. ... This short yet very accessible book written by three leading experts in the field contains many examples, including explicit reproducible computations with their open source Mat lab toolbox NCSOS tools. It can be recommended to young researchers with an interest in polynomial optimization.” (Didier Henrion, Mathematical Reviews, May, 2017)