000			01966nam 2200349| 4500
001			84597
005			20220202143505.0
010			_a978-3-319-33338-0 _dcompra
090			_a84597
100			_a20190128d2016 k||y0pory50 ba
101			_aeng
102			_aCH
200			_aOptimization of polynomials in non-commuting variables _bDocumento eletrónico _fSabine Burgdorf, Igor Klep, Janez Povh
210			_aCham _cSpringer International Publishing _d2016
215			_aXV, 104 p. _cil.
225			_aSpringerBriefs in Mathematics
300			_aColocação: Online
303			_aThis 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.
410			_x2191-8198
606			_aGeometria algébrica
606			_aProgramação de computadores
606			_aTeoria dos sistemas
680			_aQA564
700			_aBurgdorf _bSabine
701			_933907 _aKlep _bIgor _4070
701			_933908 _aPovh _bJanez _4070
801			_gRPC _aPT
856			_uhttps://doi.org/10.1007/978-3-319-33338-0
942			_2lcc _cF _n0