On error bounds for lower semicontinuous functions

Zili Wu*, Jane J. Ye

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

82 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)301-314
Number of pages14
JournalMathematical Programming, Series B
Issue number2
Publication statusPublished - Apr 2002
Externally publishedYes


  • Global error bound
  • Local error bound
  • Lower Dini derivative
  • Subdifferential

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