A sum of squares approximation of nonnegative polynomials

2004/12/20 by Jean B. Lasserre, Lasserre, Jean B. · 2 citations
Mathematics · #11E25 #12D15 #12Y05 #13P05 #90C22 #90C25 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:11E25 #msc:12D15 #msc:12Y05 #msc:13P05 #msc:90C22 #msc:90C25

paper · pdf · doi:10.48550/arxiv.math/0412398

arxiv created 2004/12/20 · arxiv updated 2009/12/01

Abstract

We show that every real nonnegative polynomial f can be approximated as closely as desired by a sequence of polynomials \f_ε\ that are sums of squares. Each f_ε has a simple et explicit form in terms of f and ε. A special representation is also obtained for convex polynomials, nonnegative on a convex semi-algebraic set.

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• Certificates for nonnegativity of multivariate integer polynomials under perturbations
• Density, Determinacy, Duality and a Regularized Moment-SOS Hierarchy

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