Representations of Non-negative Polynomials via the Critical Ideals
نویسنده
چکیده
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].
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