EAN: 9783319333366

SPRINGERBRIEFS IN MATHEMATICS OPTIMIZATION OF...

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.

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