A sufficient condition for local nonnegativity

10/29/2019

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by   Jia Xu, et al.

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A real polynomial f is called local nonnegative at a point p, if it is nonnegative in a neighbourhood of p. In this paper, a sufficient condition for determining this property is constructed. Newton's principal part of f (denoted as f_N) plays a key role in this process. We proved that if every F-face, (f_N)_F, of f_N is strictly positive over (ℝ∖ 0)^n, then f is local nonnegative at the origin O.