Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/23989
Title: Equivalent conditions for local error bounds
Authors: Meng, KW
Yang, XQ 
Keywords: Error bounds
Normal cones
Strong slope
Subderivative
Subdifferential
Issue Date: 2012
Publisher: Springer
Source: Set-valued and variational analysis, 2012, v. 20, no. 4, p. 617-636 How to cite?
Journal: Set-Valued and Variational Analysis 
Abstract: In this paper we present two classes of equivalent conditions for local error bounds in finite dimensional spaces. We formulate conditions of the first class by using subderivatives, subdifferentials and strong slopes for nearby points outside the referenced set, and show that these conditions actually characterize a uniform version of the local error bound property. We demonstrate this uniformity for the max function of a finite collection of smooth functions, and as a consequence we show that quasinormality constraint qualifications guarantee the existence of local error bounds. We further present the second class of equivalent conditions for local error bounds by using the various limits defined on the boundary of the referenced set. In presenting these conditions, we exploit the variational geometry of the referenced set in a systematic way and unify some existing results in the literature.
URI: http://hdl.handle.net/10397/23989
DOI: 10.1007/s11228-012-0217-0
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