Generalized semi-infinite programming: A tutorial

F. Guerra Vázques, J.J. Rückmann, O. Stein, Georg J. Still

Research output: Contribution to journalArticleAcademicpeer-review

51 Citations (Scopus)
33 Downloads (Pure)

Abstract

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.
Original languageEnglish
Pages (from-to)394-419
Number of pages26
JournalJournal of computational and applied mathematics
Volume217
Issue number2
DOIs
Publication statusPublished - 2008

Keywords

  • Robust optimization
  • Structure of the feasible set
  • Reduction ansatz
  • Numerical methods
  • Generalized semi-infinite programming
  • Design centering
  • First- and second-order optimality conditions

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