Abstract
In this paper, we introduce the exact tangent approximation property for a convex set and provide its characterizations, including the nonzero extent of a convex set. We obtain necessary and sufficient conditions for the closedness of the positive hull of a convex set via a limit set defined by truncated upper level sets of the gauge function. We also apply the exact tangent approximation property to study the existence of a global error bound for a proper, lower semicontinuous and positively homogeneous function.
Original language | English |
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Pages (from-to) | 123-137 |
Number of pages | 15 |
Journal | Journal of Optimization Theory and Applications |
Volume | 164 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Jan 2014 |
Keywords
- Error bounds
- Extent of a convex set
- Gauge functions
- Positive hull
- Positively homogeneous functions
- Support functions
- Tangent approximation
ASJC Scopus subject areas
- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics