Burgdorf / Klep / Povh Optimization of Polynomials in Non-Commuting Variables

1. Auflage 2016
ISBN: 978-3-319-33338-0
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 104 Seiten, eBook

Reihe: 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.

Zielgruppe

Research

Autoren/Hrsg.

Burgdorf, Sabine

Klep, Igor

Povh, Janez

Inhaltsverzeichnis

-1. Selected results from algebra and mathematical optimization. -2. Detecting sums of hermitian squares. -3. Cyclic equivalence to sums of hermitian squares. -4. Eigenvalue optimization of polynomials in non-commuting variables. -5. Trace optimization of polynomials in non-commuting variables. –References. –Index.