Fedoryuk values and stability of global H\"{o}lderian error bounds for polynomial functions

Let $f$ be a polynomial function of $n$ variables. In this paper, we study stability of global H"{o}lderian error bound for a nonempty sublevel set $[f \le t]$underaperturbationof$t$. In this paper, we give:

• Criteria for the existence of a global H"{o}lderian error bound of $[f \le t]$;
• Formulas for computing explicitly the set $$H(f):=\{t\in \mathbb{R}:[f\le t]\text{has a global H}\ddot{\text{o}}\text{lderian error bound}\}$$ via some Fedoryuk values of $f$ and definition of threshold for the existence of global H"{o}lderian error bound of $f$;
• Definition of all types of stability of global H"{o}lderian error bound of $[f\le t]$.