Optimization of Polynomials in Non-Commuting Variables
Springer International Publishing (Verlag)
978-3-319-33336-6 (ISBN)
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.
-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.
"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)
“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)
| Erscheinungsdatum | 11.07.2016 |
|---|---|
| Reihe/Serie | SpringerBriefs in Mathematics |
| Zusatzinfo | XV, 104 p. 2 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Informatik ► Theorie / Studium |
| Mathematik / Informatik ► Mathematik ► Computerprogramme / Computeralgebra | |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Wirtschaft ► Betriebswirtschaft / Management | |
| Schlagworte | Algebraic Geometry • Extracting optimizers • free analysis • free real algebraic geometry • Mathematical Optimization • mathematical software • mathematics and statistics • Newton chip method • Newton cyclic chip method • non-commutative algebraic geometry • Operations Research, Management Science • polynomial data • Quantum Computing • Quantum Information Science • quantum mechanics • Quantum Theory • semidefinite programming • Sum of hermitian squares • Systems Theory, Control • Unconstrained optimization |
| ISBN-10 | 3-319-33336-4 / 3319333364 |
| ISBN-13 | 978-3-319-33336-6 / 9783319333366 |
| Zustand | Neuware |
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