Semi-infinite optimization: structure and stability of the feasible set

H.Th. Jongen, F. Twilt, G.W. Weber

Research output: Contribution to journalArticleAcademicpeer-review

61 Citations (Scopus)
114 Downloads (Pure)

Abstract

The problem of the minimization of a functionf: ℝn→ℝ under finitely many equality constraints and perhaps infinitely many inequality constraints gives rise to a structural analysis of the feasible setM[H, G]={x∈ℝn¦H(x)=0,G(x, y)≥0,y∈Y} with compactY⊂ℝr. An extension of the well-known Mangasarian-Fromovitz constraint qualification (EMFCQ) is introduced. The main result for compactM[H, G] is the equivalence of the topological stability of the feasible setM[H, G] and the validity of EMFCQ. As a byproduct, we obtain under EMFCQ that the feasible set admits local linearizations and also thatM[H, G] depends continuously on the pair (H, G). Moreover, EMFCQ is shown to be satisfied generically.
Original languageEnglish
Pages (from-to)529-552
Number of pages0
JournalJournal of optimization theory and applications
Volume72
Issue number3
DOIs
Publication statusPublished - 1992

Keywords

  • reduction principle
  • IR-85875
  • Genericity
  • METIS-140348
  • Structure of the feasible set
  • topological stability
  • Semi-infinite optimization

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