Real Algebraic and Analytic Geometry
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297. Dang Tuan Hiep:
Representation of non-negative polynomials via the KKT ideals.

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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).

Full text, 8p.: dvi 41k, ps.gz 279k, pdf 306k.