- Title
- On local coincidence of a convex set and its tangent cone
- Creator
- Meng, Kaiwen; Roshchina, Vera; Yang, Xiaoqi
- Date
- 2015
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/92669
- Identifier
- vital:9619
- Identifier
-
https://doi.org/10.1007/s10957-014-0582-y
- Identifier
- ISSN:0022-3239
- 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.
- Publisher
- Springer/Plenum Publishers
- Relation
- Journal of Optimization Theory and Applications Vol. 164, no. 1 (2015), p. 123-137
- Rights
- Copyright © Springer Science+Business Media New York 2014
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0102 Applied Mathematics; 0103 Numerical and Computational Mathematics; 0906 Electrical and Electronic Engineering; Tangent approximation; Extent of a convex set; Positive hull; Error bounds; Support functions; Gauge functions; Positively homogeneous functions
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