Please use this identifier to cite or link to this item: http://localhost/handle/Hannan/309183
Title: Optimization of Polynomials in Non-Commuting Variables /
Authors: Burgdorf, Sabine. ;;Klep, Igor. ;;Povh, Janez. ;
subject: Mathematics;Geometry, Algebraic. ;sh85054140. ;;System theory. ;sh85131743. ;;Computer software. ;sh85029534. ;;Quantum computers. ;sh98002795. ;;Operations research. ;sh85095020. ;;Management science. ;sh85080363. ;;Mathematics;Geometry, Algebraic. ;sh85054140. ;;Quantum computing. ;sh2014002839. ;;Operations Research, Management Science. ;;Mathematical Software. ;;Systems Theory, Control. ;;516.35 ; 23 ;;QA564-609 ;
Year: 2016
place: Cham :
Publisher: Springer International Publishing :
Imprint: Springer,
Series/Report no.: SpringerBriefs in Mathematics, ; 2191-8198. ;
SpringerBriefs in mathematics. ; 2191-8198 ;no2011133396. ;
Abstract: 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. ;
Description: 



Printed edition: ; 9783319333366. ;

URI: http://46.100.53.162/handle/Ebook/140068
http://46.100.53.162/handle/Ebook/35900
http://localhost/handle/Hannan/309183
ISBN: 9783319333380 ;
9783319333366 (print) ;
Appears in Collections:Finance

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Title: Optimization of Polynomials in Non-Commuting Variables /
Authors: Burgdorf, Sabine. ;;Klep, Igor. ;;Povh, Janez. ;
subject: Mathematics;Geometry, Algebraic. ;sh85054140. ;;System theory. ;sh85131743. ;;Computer software. ;sh85029534. ;;Quantum computers. ;sh98002795. ;;Operations research. ;sh85095020. ;;Management science. ;sh85080363. ;;Mathematics;Geometry, Algebraic. ;sh85054140. ;;Quantum computing. ;sh2014002839. ;;Operations Research, Management Science. ;;Mathematical Software. ;;Systems Theory, Control. ;;516.35 ; 23 ;;QA564-609 ;
Year: 2016
place: Cham :
Publisher: Springer International Publishing :
Imprint: Springer,
Series/Report no.: SpringerBriefs in Mathematics, ; 2191-8198. ;
SpringerBriefs in mathematics. ; 2191-8198 ;no2011133396. ;
Abstract: 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. ;
Description: 



Printed edition: ; 9783319333366. ;

URI: http://46.100.53.162/handle/Ebook/140068
http://46.100.53.162/handle/Ebook/35900
http://localhost/handle/Hannan/309183
ISBN: 9783319333380 ;
9783319333366 (print) ;
Appears in Collections:Finance

Files in This Item:
File Description SizeFormat 
9783319333380.pdf1.49 MBAdobe PDFThumbnail
Preview File
Title: Optimization of Polynomials in Non-Commuting Variables /
Authors: Burgdorf, Sabine. ;;Klep, Igor. ;;Povh, Janez. ;
subject: Mathematics;Geometry, Algebraic. ;sh85054140. ;;System theory. ;sh85131743. ;;Computer software. ;sh85029534. ;;Quantum computers. ;sh98002795. ;;Operations research. ;sh85095020. ;;Management science. ;sh85080363. ;;Mathematics;Geometry, Algebraic. ;sh85054140. ;;Quantum computing. ;sh2014002839. ;;Operations Research, Management Science. ;;Mathematical Software. ;;Systems Theory, Control. ;;516.35 ; 23 ;;QA564-609 ;
Year: 2016
place: Cham :
Publisher: Springer International Publishing :
Imprint: Springer,
Series/Report no.: SpringerBriefs in Mathematics, ; 2191-8198. ;
SpringerBriefs in mathematics. ; 2191-8198 ;no2011133396. ;
Abstract: 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. ;
Description: 



Printed edition: ; 9783319333366. ;

URI: http://46.100.53.162/handle/Ebook/140068
http://46.100.53.162/handle/Ebook/35900
http://localhost/handle/Hannan/309183
ISBN: 9783319333380 ;
9783319333366 (print) ;
Appears in Collections:Finance

Files in This Item:
File Description SizeFormat 
9783319333380.pdf1.49 MBAdobe PDFThumbnail
Preview File