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

## TL;DR

This paper investigates the stability of global H"olderian error bounds for polynomial functions, providing criteria, explicit formulas involving Fedoryuk values, and classifications of stability types under perturbations.

## Contribution

It introduces criteria and explicit formulas for the existence and stability of global H"olderian error bounds for polynomial sublevel sets, using Fedoryuk values.

## Key findings

- Criteria for existence of global H"olderian error bounds.
- Explicit formulas for the set of thresholds with error bounds.
- Classification of stability types for error bounds.

## Abstract

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 $[f \le t]$ under a perturbation of $t$. 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 $$H(f) := \{ t \in \mathbb{R}: [f \le t]\ \text{has a global H\"{o}lderian error bound}\}$$ 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 $[f \le t]$.