Representation of nonnegative convex polynomials

Jean B. Lasserre(lasserrelaas.fr)

Abstract: We provide a specific representation of convex polynomials nonnegative on a convex (not necessarily compact) basic closed semi-algebraic set $K$ of $R^n$. Namely, they belong to a specific subset of the quadratic module generated by the concave polynomials that define $K$.

Keywords: Convexity; basi semi-algebraic sets.

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Citation: To appear in Archiv der Mathematik

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Entry Submitted: 07/09/2008
Entry Accepted: 07/09/2008
Entry Last Modified: 07/09/2008

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