Constrained polynomial optimization problems with noncommuting variables
type: Item
instance of: scholarly article
zbMATH Open document ID: 1263.90052
DOI: 10.1137/110830733
author: Kristijan Cafuta
author: Igor Klep
author: Janez Povh
published in: SIAM Journal on Optimization
publication date: 2012-09-12T00:00:00Z
Mathematics Subject Classification ID: 90C22
Mathematics Subject Classification ID: 14P10
zbMATH DE Number: 6081228
zbMATH Keywords: polynomial optimization
zbMATH Keywords: noncommutative algebra
describes a project that uses: NCAlgebra
describes a project that uses: SparsePOP
describes a project that uses: GloptiPoly
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1137/110830733
OpenAlex ID: W2033316317
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title: Constrained polynomial optimization problems with noncommuting variables
review text: Motivated by applications in control theory and systems engineering, the authors extend existing results on unconstrained polynomial optimization with noncommutating variables to the case of polydisc and ball constraints. They show that a noncommutative (nc) polynomial is nonnegative on these sets if and only if it is a sum of squares. As a consequence of this property, when solving nc polynomial optimization problems, there is need to construct a whole hierarchy of semidefinite programming (SDP) problems, optima can be obtained via a single SDP problem. This is in sharp contrast with the commutative case.
reviewed by: Didier Henrion
description: scientific article; zbMATH DE number 6081228