REPRESENTATION OF NON-NEGATIVE POLYNOMIALS VIA THE KKT IDEALS

This paper studies the representation of a non-negative polynomial f on a non-compact semi-algebraic set K modulo its KKT (Karush-KuhnTucker) 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 ≥ 0 on K.

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