Perturbed or optimization in banach spaces I: A general theory based on a weak directional constraint qualification

J. Frédéric Bonnans, Roberto Cominetti

Research output: Contribution to journalArticlepeer-review

26 Scopus citations

Abstract

Using a directional form of constraint qualification weaker than Robinson's, we derive an implicit function theorem for inclusions and use it for first- and second-order sensitivity analyses of the value function in perturbed constrained optimization. We obtain Hölder and Lipschitz properties and, under a no-gap condition, first-order expansions for exact and approximate solutions. As an application, differentiability properties of metric projections in Hilbert spaces are obtained, using a condition generalizing polyhedricity. We also present in the appendix a short proof of a generalization of the convex duality theorem in Banach spaces.

Original languageEnglish
Pages (from-to)1151-1171
Number of pages21
JournalSIAM Journal on Control and Optimization
Volume34
Issue number4
DOIs
StatePublished - Jul 1996

Keywords

  • Approximate solutions
  • Convex duality
  • Directional constraint qualification
  • Marginal function
  • Regularity and implicit function theorems
  • Sensitivity analysis

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