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Title: On local coincidence of a convex set and its tangent cone
Authors: Meng, KW
Roshchina, V
Yang, XQ 
Keywords: Tangent approximation
Extent of a convex set
Positive hull
Error bounds
Support functions
Gauge functions
Positively homogeneous functions
Issue Date: 2015
Publisher: Springer
Source: Journal of optimization theory and applications, 2015, v. 164, no. 1, p. 123-137 How to cite?
Journal: Journal of optimization theory and applications 
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.
ISSN: 0022-3239 (print)
1573-2878 (online)
DOI: 10.1007/s10957-014-0582-y
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