Fedoryuk values and stability of global Hölderian error bounds for polynomial functions

Abstract

Let $f$ be a polynomial function of $n$ variables. In this paper, we study stability of global Hölderian error bound for a nonempty sublevel set $[f\le t]$ under a perturbation of $t$. In this paper, we give: * Criteria for the existence of a global Hölderian error bound of $[f\le t]$; * Formulas for computing explicitly the set $$H(f):=\{t\in \mathbb{R}:[f\le t]\text{has a global Ho¨lderian error bound}\}$$ via some Fedoryuk values of $f$ and definition of threshold for the existence of global Hölderian error bound of $f$; * Definition of all types of stability of global Hölderian error bound of $[f\le t]$.

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