Characterization of the robust isolated calmness for a class of conic programming problems

C. Ding, Defeng Sun, L. Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

27 Citations (Scopus)


This paper is devoted to studying the robust isolated calmness of the Karush- Kuhn-Tucker (KKT) solution mapping for a large class of interesting conic programming problems (including most commonly known ones arising from applications) at a locally optimal solution. Under the Robinson constraint qualification, we show that the KKT solution mapping is robustly isolated calm if and only if both the strict Robinson constraint qualification and the second order sufficient condition hold. This implies, among others, that at a locally optimal solution the second order sufficient condition is needed for the KKT solution mapping to have the Aubin property.
Original languageEnglish
Pages (from-to)67-90
Number of pages24
JournalSIAM Journal on Optimization
Issue number1
Publication statusPublished - 1 Jan 2017
Externally publishedYes


  • Aubin property
  • C2-cone reducible sets
  • Robust isolated calmness
  • Second order sufficient condition
  • Stability
  • Strict Robinson constraint qualification

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science


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