Optimization of Polynomials in Non-Commuting Variables - Brossura

Burgdorf, Sabine; Klep, Igor; Povh, Janez

Brossura

ISBN 10: 3319333364 ISBN 13: 9783319333366

Casa editrice: Springer, 2016

Riassunto

This bookpresents recent results on positivity and optimization of polynomials innon-commuting variables. Researchers in non-commutative algebraic geometry,control theory, system engineering, optimization, quantum physics andinformation science will find the unified notation and mixture of algebraicgeometry and mathematical programming useful. Theoretical results are matchedwith algorithmic considerations; several examples and information on how to useNCSOStools open source package to obtain the results provided. Results arepresented on detecting the eigenvalue and trace positivity of polynomials innon-commuting variables using Newton chip method and Newton cyclic chip method,relaxations for constrained and unconstrained optimization problems, semidefiniteprogramming formulations of the relaxations and finite convergence of thehierarchies of these relaxations, and the practical efficiency of algorithms.

Su questo libro

Recensione

“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)

Dettagli dell?edizione

• Editore: Springer
• Data di pubblicazione: 2016
• ISBN 10: 3319333364
• ISBN 13: 9783319333366
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero edizione: 1
• Numero di pagine: 120