On Local Coincidence of a Convex Set and its Tangent Cone

Kaiwen Meng (), Vera Roshchina () and Xiaoqi Yang ()
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Kaiwen Meng: Southwest Jiaotong University
Vera Roshchina: Federation University Australia
Xiaoqi Yang: The Hong Kong Polytechnic University

Journal of Optimization Theory and Applications, 2015, vol. 164, issue 1, No 6, 123-137

Abstract: 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.

Keywords: Tangent approximation; Extent of a convex set; Positive hull; Error bounds; Support functions; Gauge functions; Positively homogeneous functions; 49J52; 49J53 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10957-014-0582-y

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