On Local Coincidence of a Convex Set and its Tangent Cone

Kaiwen Meng, Vera Roshchina, Xiaoqi Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

6 Citations (Scopus)


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 languageEnglish
Pages (from-to)123-137
Number of pages15
JournalJournal of Optimization Theory and Applications
Issue number1
Publication statusPublished - 1 Jan 2014


  • 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


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