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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Received: April 27, 2001 / Accepted: November 6, 2001¶Published online April 12, 2002
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Wu, Z., Ye, J. On error bounds for lower semicontinuous functions. Math. Program. 92, 301–314 (2002). https://doi.org/10.1007/s101070100278
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DOI: https://doi.org/10.1007/s101070100278