03714nam 22007095 450 991025408540332120200630120206.03-319-33338-010.1007/978-3-319-33338-0(CKB)3710000000726843(DE-He213)978-3-319-33338-0(MiAaPQ)EBC4543269(PPN)194379914(EXLCZ)99371000000072684320160607d2016 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierOptimization of Polynomials in Non-Commuting Variables /by Sabine Burgdorf, Igor Klep, Janez Povh1st ed. 2016.Cham :Springer International Publishing :Imprint: Springer,2016.1 online resource (XV, 104 p. 2 illus. in color.)SpringerBriefs in Mathematics,2191-81983-319-33336-4 Includes bibliographical references at the end of each chapters and index.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.SpringerBriefs in Mathematics,2191-8198Geometry, AlgebraicQuantum computersOperations researchManagement scienceComputer softwareSystem theoryAlgebraic Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11019Quantum Computinghttps://scigraph.springernature.com/ontologies/product-market-codes/M14070Operations Research, Management Sciencehttps://scigraph.springernature.com/ontologies/product-market-codes/M26024Mathematical Softwarehttps://scigraph.springernature.com/ontologies/product-market-codes/M14042Systems Theory, Controlhttps://scigraph.springernature.com/ontologies/product-market-codes/M13070Geometry, Algebraic.Quantum computers.Operations research.Management science.Computer software.System theory.Algebraic Geometry.Quantum Computing.Operations Research, Management Science.Mathematical Software.Systems Theory, Control.519.3Burgdorf Sabineauthttp://id.loc.gov/vocabulary/relators/aut756027Klep Igorauthttp://id.loc.gov/vocabulary/relators/autPovh Janezauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910254085403321Optimization of Polynomials in Non-Commuting Variables2129510UNINA