The Algebraic Degree of Semidefinite Programming

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dc.creatorNie, Jiawang
dc.creatorRanestad, Kristian
dc.creatorSturmfels, Bernd
dc.date2006-11-19
dc.date2008-09-08
dc.date.accessioned2026-07-07T10:01:06Z
dc.date.available2026-07-07T10:01:06Z
dc.descriptionGiven a generic semidefinite program, specified by matrices with rational entries, each coordinate of its optimal solution is an algebraic number. We study the degree of the minimal polynomials of these algebraic numbers. Geometrically, this degree counts the critical points attained by a linear functional on a fixed rank locus in a linear space of symmetric matrices. We determine this degree using methods from complex algebraic geometry, such as projective duality, determinantal varieties, and their Chern classes.
dc.description23 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/math/0611562
dc.identifierhttp://arxiv.org/abs/math/0611562
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/168526
dc.subjectOptimization and Control
dc.subjectAlgebraic Geometry
dc.titleThe Algebraic Degree of Semidefinite Programming
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