On generalized semi-infinite optimization and bilevel optimization

Oliver Stein, Georg J. Still

Research output: Contribution to journalArticleAcademicpeer-review

76 Citations (Scopus)
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The paper studies the connections and differences between bilevel problems (BL) and generalized semi-infinite problems (GSIP). Under natural assumptions (GSIP) can be seen as a special case of a (BL). We consider the so-called reduction approach for (BL) and (GSIP) leading to optimality conditions and Newton-type methods for solving the problems. We show by a structural analysis that for (GSIP)-problems the regularity assumptions for the reduction approach can be expected to hold generically at a solution but for general (BL)-problems not. The genericity behavior of (BL) and (GSIP) is in particular studied for linear problems.
Original languageEnglish
Pages (from-to)444-462
JournalEuropean journal of operational research
Issue number3
Publication statusPublished - 2002


  • IR-74650
  • METIS-208601
  • Genericity behavior
  • Optimality conditions
  • Numerical methods
  • Semi-infinite programming
  • Bilevel programming


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