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- W2912641151 abstract "Let $f$ be a polynomial function of $n$ variables. In this paper, we study stability of global Holderian error bound for a sublevel set $[f le t]$ under a perturbation of $t$. Namely, we investigate the following questions: 1. Suppose that $[f le t]$ has a global Holderian error bound, when does there exist an open interval $I(t) subset mathbb{R}, t in I(t)$, such that for any $t' in I(t)$, $[f le t']$ has also a global Holderian error bound? 2. Suppose that $[f le t]$ does not have global Holderian error bound, when does there exist an open interval $I(t) subset mathbb{R}, t in I(t)$, such that for any $t' in I(t)$, $[f le t']$ does also not have global Holderian error bound? 3. Are there other types of stability which are different from types in questions 1 and 2? To answer these questions, we compute the set $H(f)$ of all values $t in mathbb{R}$ such that $[f le t]$ has a global Holderian error bound and study the relationship between $H(f)$ and the set of Palais-Smale values of $f$. Our main results are the following: * The list of all possible types of stability is given; * For an arbitrary $t in mathbb{R}$, we can determine the type of stability of global Holderian error bound for $[f le t]$." @default.
- W2912641151 created "2019-02-21" @default.
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- W2912641151 date "2019-02-15" @default.
- W2912641151 modified "2023-09-27" @default.
- W2912641151 title "Palais-Smale values and stability of global H{o}lderian error bounds for polynomial functions" @default.
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