On Local Coincidence of a Convex Set and its Tangent Cone

Kaiwen Meng; Vera Roshchina; Xiaoqi Yang

doi:10.1007/s10957-014-0582-y

On Local Coincidence of a Convex Set and its Tangent Cone

Kaiwen Meng, Vera Roshchina, Xiaoqi Yang

Research output: Journal article publication › Journal article › Academic research › peer-review

4 Citations (Scopus)

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
Pages (from-to)	123-137
Number of pages	15
Journal	Journal of Optimization Theory and Applications
Volume	164
Issue number	1
DOIs	https://doi.org/10.1007/s10957-014-0582-y
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

More information

10.1007/s10957-014-0582-y

Scopus Link

Cite this

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KW - Positively homogeneous functions

KW - Support functions

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