Minimizing Polynomial Functions

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dc.creatorParrilo, Pablo A.
dc.creatorSturmfels, Bernd
dc.date2001-03-26
dc.date.accessioned2026-07-07T04:40:46Z
dc.date.available2026-07-07T04:40:46Z
dc.descriptionWe compare algorithms for global optimization of polynomial functions in many variables. It is demonstrated that existing algebraic methods (Gröbner bases, resultants, homotopy methods) are dramatically outperformed by a relaxation technique, due to N.Z. Shor and the first author, which involves sums of squares and semidefinite programming. This opens up the possibility of using semidefinite programming relaxations arising from the Positivstellensatz for a wide range of computational problems in real algebraic geometry. This paper was presented at the Workshop on Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science, held at DIMACS, Rutgers University, March 12-16, 2001.
dc.descriptionThis paper was presented at the Workshop on Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science, held at DIMACS, Rutgers University, March 12-16, 2001
dc.identifierhttps://arxiv.org/abs/math/0103170
dc.identifierhttp://arxiv.org/abs/math/0103170
dc.identifierAlgorithmic and quantitative real algebraic geometry, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 60, pp. 83--99, AMS, 2003. ISBN: 0-8218-2863-0.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61143
dc.subjectOptimization and Control
dc.subjectCommutative Algebra
dc.subjectAlgebraic Geometry
dc.subject13J30, 90C22, 13P10, 65H10
dc.titleMinimizing Polynomial Functions
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