Minimizing Polynomials Over Semialgebraic Sets

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dc.creatorNie, Jiawang
dc.creatorDemmel, James W.
dc.creatorPowers, Victoria
dc.date2005-02-17
dc.date.accessioned2026-07-07T05:17:08Z
dc.date.available2026-07-07T05:17:08Z
dc.descriptionThis paper concerns a method for finding the minimum of a polynomial on a semialgebraic set, i.e., a set in $\re^m$ defined by finitely many polynomial equations and inequalities, using the Karush-Kuhn-Tucker (KKT) system and sum of squares (SOS) relaxations. This generalizes results in the recent paper \cite{njw_grad}, which considers minimizing polynomials on algebraic sets, i.e., sets in $\re^m$ defined by finitely many polynomial equations. Most of the theorems and conclusions in \cite{njw_grad} generalize to semialgebraic sets, even in the case where the semialgebraic set is not compact. We discuss the method in some special cases, namely, when the semialgebraic set is contained in the nonnegative orthant $\re^n_+$ or in box constraints $[a,b]_n$. These constraints make the computations more efficient.
dc.identifierhttps://arxiv.org/abs/math/0502391
dc.identifierhttp://arxiv.org/abs/math/0502391
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74243
dc.subjectOptimization and Control
dc.subjectAlgebraic Geometry
dc.titleMinimizing Polynomials Over Semialgebraic Sets
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