 |
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| Volume 6, Number 1, January 2010, pp. 177-186 | ||||||||
| Hui Hu and Qing Wang | ||||||||
| Key words: | ||||||||
| convex inequalities, equal closure property, local and global error bounds | ||||||||
| Mathematices Subject Classification: 90C, 90C25 | ||||||||
|
||||||||
| Volume 6, Number 1, January 2010, pp. 177-186 | ||||||||
| Hui Hu and Qing Wang | ||||||||
| Key words: | ||||||||
| convex inequalities, equal closure property, local and global error bounds | ||||||||
| Mathematices Subject Classification: 90C, 90C25 | ||||||||
|
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| Abstract: | |||
| This paper studies local and global error bounds for an inequality defined by a proper function without assuming lower semicontinuity. The relationship between error bounds of the given function and its closure is established through ``bridge" theorems. The equal closure property is introduced and shown to be critical in this establishment. Applying the bridge theorems to exterior characterizations valid for a lower semicontinuous function, one can obtain characterizations for a proper function. | |||
| Local and global error bounds for proper functions | ||