Representations of non-negative polynomials via critical ideals

Details Representations of non-negative polynomials via critical ideals Representations of non-negative polynomials via critical ideals

2011-12-17

arxiv.org/abs/1112.4072v1

Mathematics

Algebraic Geometry

14 pages

Scientific paper

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 assumptions 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 $f\ge 0$ on $K$. In particular, we focus on the polynomial ring $\mathbb R[x]$.

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