Real Algebraic and Analytic Geometry Preprint Server

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Submission: 2010, January 7.

Abstract:
This paper studies the representation of a non-negative polynomial $f$ on a non-compact semi-algebraic set $K$ modulo its KKT (Karush-Kuhn-Tucker) ideal. Under the assumption that $f$ satisfies the boundary Hessian conditions (BHC) at each zero of $f$ in $K$; we show that $f$ can be represented as a sum of squares (SOS) of real polynomials modulo its KKT ideal if $f\ge 0$ on $K$.

Mathematics Subject Classification (2000): 13J30, 11E25, 14P10, 90C22.

Keywords and Phrases: Non-negative polynomials, Sum of Squares (SOS), Optimization of Polynomials, Semidefinite Programming (SDP).

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