Generalized semi-infinite programming: A tutorial

F Guerra-Vazquez, Jan-Joachim Ruckmann, O Stein, G Still

Research output: Contribution to journalArticle

51 Citations (Scopus)


This tutorial presents an introduction to generalized semi-infinite programming (GSIP) which in recent years became a vivid field of active research in mathematical programming. A GSIP problem is characterized by an infinite number of inequality constraints, and the corresponding index set depends additionally on the decision variables. There exist a wide range of applications which give rise to GSIP models; some of them are discussed in the present paper. Furthermore, geometric and topological properties of the feasible set and, in particular, the difference to the standard semi-infinite case are analyzed. By using first-order approximations of the feasible set corresponding constraint qualifications are developed. Then, necessary and sufficient first- and second-order optimality conditions are presented where directional differentiability properties of the optimal value function of the so-called lower level problem are used. Finally, an overview of numerical methods is given. (C) 2007 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)394-419
Number of pages26
JournalJournal of Computational and Applied Mathematics
Issue number2
Publication statusPublished - 1 Aug 2008


  • design centering
  • structure of the feasible set
  • reduction ansatz
  • first- and second-order optimality conditions
  • generalized semi-infinite programming
  • robust optimization
  • numerical methods


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