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Statements

Subject Item: dbr:Hilbert's_seventeenth_problem
dbo:wikiPageWikiLink: dbr:SOS-convexity

Subject Item: dbr:Polynomial_SOS
dbo:wikiPageWikiLink: dbr:SOS-convexity

Subject Item: dbr:SOS-convexity
rdfs:label: SOS-convexity
rdfs:comment: A multivariate polynomial is SOS-convex (or sum of squares convex) if its Hessian matrix H can be factored as H(x) = ST(x)S(x) where S is a matrix (possibly rectangular) which entries are polynomials in x. In other words, the Hessian matrix is a SOS matrix polynomial. An equivalent definition is that the form defined as g(x,y) = yTH(x)y is a sum of squares of forms.
dcterms:subject: dbc:Real_algebraic_geometry dbc:Convex_analysis dbc:Homogeneous_polynomials
dbo:wikiPageID: 64465650
dbo:wikiPageRevisionID: 1117679243
dbo:wikiPageWikiLink: dbr:Semidefinite_programming dbr:Hilbert's_seventeenth_problem dbr:Non-constructive dbr:Polynomial_SOS dbc:Homogeneous_polynomials dbr:Multivariate_polynomial dbr:Pablo_Parrilo dbr:Amir_Ali_Ahmadi dbc:Convex_analysis dbr:Hessian_matrix dbc:Real_algebraic_geometry dbr:Sum-of-squares_optimization
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dbo:abstract: A multivariate polynomial is SOS-convex (or sum of squares convex) if its Hessian matrix H can be factored as H(x) = ST(x)S(x) where S is a matrix (possibly rectangular) which entries are polynomials in x. In other words, the Hessian matrix is a SOS matrix polynomial. An equivalent definition is that the form defined as g(x,y) = yTH(x)y is a sum of squares of forms.
prov:wasDerivedFrom: wikipedia-en:SOS-convexity?oldid=1117679243&ns=0
dbo:wikiPageLength: 4811
foaf:isPrimaryTopicOf: wikipedia-en:SOS-convexity

Subject Item: dbr:Sos-convex
dbo:wikiPageWikiLink: dbr:SOS-convexity
dbo:wikiPageRedirects: dbr:SOS-convexity

Subject Item: wikipedia-en:SOS-convexity
foaf:primaryTopic: dbr:SOS-convexity