Constrained polynominal optimization problems with noncommuting variables


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CAFUTA, Kristijan, Igor KLEP, Janez POVH, 2011. Constrained polynominal optimization problems with noncommuting variables

@techreport{Cafuta2011Const-15283, series={Konstanzer Schriften in Mathematik}, title={Constrained polynominal optimization problems with noncommuting variables}, year={2011}, number={285}, author={Cafuta, Kristijan and Klep, Igor and Povh, Janez} }

<rdf:RDF xmlns:dcterms="" xmlns:dc="" xmlns:rdf="" xmlns:bibo="" xmlns:dspace="" xmlns:foaf="" xmlns:void="" xmlns:xsd="" > <rdf:Description rdf:about=""> <dc:creator>Cafuta, Kristijan</dc:creator> <dc:contributor>Povh, Janez</dc:contributor> <dcterms:rights rdf:resource=""/> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dc:rights>terms-of-use</dc:rights> <bibo:uri rdf:resource=""/> <dc:contributor>Cafuta, Kristijan</dc:contributor> <dcterms:hasPart rdf:resource=""/> <dc:creator>Povh, Janez</dc:creator> <dc:date rdf:datatype="">2011-09-02T11:10:17Z</dc:date> <dc:contributor>Klep, Igor</dc:contributor> <dspace:isPartOfCollection rdf:resource=""/> <dc:language>eng</dc:language> <dspace:hasBitstream rdf:resource=""/> <dcterms:isPartOf rdf:resource=""/> <dcterms:available rdf:datatype="">2011-09-02T11:10:17Z</dcterms:available> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dc:creator>Klep, Igor</dc:creator> <dcterms:abstract xml:lang="eng">In this paper we study constrained eigenvalue optimization of noncommutative (nc) polynomials, focusing on the polydisc and the ball. Our three main results are as follows: (1) an nc polynomial is nonnegative if and only if it admits a weighted sum of hermitian squares decomposition; (2) (eigenvalue) optima for nc polynomials can be computed using a single semide nite program (SDP) { this sharply contrasts the commutative case where sequences of SDPs are needed; (3) the dual solution to this \single" SDP can be exploited to extract eigenvalue optimizers with an algorithm based on two ingredients: solution to a truncated nc moment problem via at extensions; Gelfand-Naimark-Segal (GNS) construction. The implementation of these procedures in our computer algebra system NCSOStools is presented and several examples pertaining to matrix inequalities are given to illustrate our results.</dcterms:abstract> <dcterms:title>Constrained polynominal optimization problems with noncommuting variables</dcterms:title> <dcterms:issued>2011</dcterms:issued> </rdf:Description> </rdf:RDF>

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