Second order optimality conditions based on parabolic second order tangent sets

J. Frédéric Bonnans, Roberto Cominetti, Alexander Shapiro

Research output: Contribution to journalArticlepeer-review

120 Scopus citations

Abstract

In this paper we discuss second order optimality conditions in optimization problems subject to abstract constraints. Our analysis is based on various concepts of second order tangent sets and parametric duality. We introduce a condition, called second order regularity, under which there is no gap between the corresponding second order necessary and second order sufficient conditions. We show that the second order regularity condition always holds in the case of semidefinite programming.

Original languageEnglish
Pages (from-to)466-492
Number of pages27
JournalSIAM Journal on Optimization
Volume9
Issue number2
DOIs
StatePublished - Mar 1999

Keywords

  • Cone constraints
  • Duality
  • Lagrange multipliers
  • Second order optimality conditions
  • Semi-infinite programming
  • Semidefinite programming
  • Tangent sets

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