On error bounds for lower semicontinuous functions

On error bounds for lower semicontinuous functions

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Article ID: iaor20031169
Country: Germany
Volume: 92
Issue: 2
Start Page Number: 301
End Page Number: 314
Publication Date: Jan 2002
Journal: Mathematical Programming
Authors: ,
Abstract:

We give some sufficient conditions for proper lower semicontinuous functions on metric spaces to have error bounds (with exponents). For a proper convex function f on a normed space X the existence of a local error bound implies that of a global error bound. If in addition X is a Banach space, then error bounds can be characterized by the subdifferential of f. In a reflexive Banach space X, we further obtain several sufficient and necessary conditions for the existence of error bounds in terms of the lower Dini derivative of f.

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