Real Algebraic and Analytic Geometry
Submission: 2010, January 19.
This paper studies the representations of a non-negative polynomial f on a non-compact semi-algebraic set K modulo its critical ideal. Under the assumption that the semi-algebraic set K is regular and 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 critical ideal if f >= 0 on K. Particularly, we only work in the polynomial ring R[X].
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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