Sufficient conditions for error bounds

Zili Wu*, Jane J. Ye

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

47 Citations (Scopus)


For a lower semicontinuous (l.s.c.) inequality system on a Banach space, it is shown that error bounds hold, provided every element in an abstract subdifferential of the constraint function at each point outside the solution set is norm bounded away from zero. A sufficient condition for a global error bound to exist is also given for an l.s.c. inequality system on a real normed linear space. It turns out that a global error bound closely relates to metric regularity, which is useful for presenting sufficient conditions for an l.s.c. system to be regular at sets. Under the generalized Slater condition, a continuous convex system on Rn is proved to be metrically regular at bounded sets.

Original languageEnglish
Pages (from-to)421-435
Number of pages15
JournalSIAM Journal on Optimization
Issue number2
Publication statusPublished - 2002
Externally publishedYes


  • Abstract subdifferentials
  • Error bounds
  • Generalized Slater condition
  • Inequality systems
  • Metrical regularity

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