On error bounds for quasinormal programs
type: Item
instance of: scholarly article
title: On error bounds for quasinormal programs
zbMATH Open document ID: 1229.90204
published in: Journal of Optimization Theory and Applications
publication date: 2011-05-11T00:00:00Z
review text: Let \(I\) and \(I_{0}\) be finite index sets, \(h_{i}:\mathbb{R}^{m}\rightarrow \mathbb{R}\) \((i\in I\cup I_{0})\) be continuously differentiable functions, and \(C:=\{y\in \mathbb{R}^{m}:h_{i}(y)\leq 0\) \((i\in I),\) \(h_{i}(y)=0\) \((i\in I_{0})\}\). The main result states that, assuming that the gradients \(\nabla h_{i}(y)\) \((i\in I\cup I_{0})\) are locally Lipschitz near \(y^{0}\in C\), if this point is quasinormal in the sense of \textit{M. R. Hestenes} [Optimization theory. The finite dimensional case. New York etc.: John Wiley\&Sons (1975; Zbl 0327.90015)] then the system defining \(C\) has the local error bound property at \(y^{0}\). An easy example for \(m=2\) shows that the converse does not hold true.
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C46
zbMATH DE Number: 5886732
zbMATH Keywords: quasinormality
zbMATH Keywords: error bound property
zbMATH Keywords: constraint qualifications
zbMATH Keywords: nonlinear optimization
author: Leonid Minchenko
author: A. N. Tarakanov
reviewed by: Juan-Enrique Martínez-Legaz
MaRDI profile type: Publication
full work available at URL: s10957-010-9768-0
OpenAlex ID: W1973879592
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DOI: 10.1007/S10957-010-9768-0
description: scientific article; zbMATH DE number 5886732