On error bounds for lower semicontinuous functions |
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Authors: | Zili Wu Jane J Ye |
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Institution: | (1) Department of Mathematics and Statistics, University of Victoria, Victoria, B.C., Canada V8W 3P4, e-mail: ziliwu@joymail.com, CA;(2) Department of Mathematics and Statistics, University of Victoria, Victoria, B.C., Canada V8W 3P4, e-mail: janeye@math.uvic.ca, CA |
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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.
Received: April 27, 2001 / Accepted: November 6, 2001?Published online April 12, 2002 |
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Keywords: | : local error bound – global error bound – subdifferential – lower Dini derivative |
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