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.
Original language | English |
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Pages (from-to) | 301-314 |
Number of pages | 14 |
Journal | Mathematical Programming, Series B |
Volume | 92 |
Issue number | 2 |
DOIs | |
Publication status | Published - Apr 2002 |
Externally published | Yes |
Keywords
- Global error bound
- Local error bound
- Lower Dini derivative
- Subdifferential