Journal of Global Optimization

, Volume 42, Issue 3, pp 413–421 | Cite as

Generalized Semi-Infinite Programming: on generic local minimizers

  • Harald Günzel
  • Hubertus Th. Jongen
  • Oliver Stein


In this paper a basic structural problem in Generalized Semi-Infinite Programming is solved. In fact, under natural and generic assumptions we show that at any (local) minimizer the “Symmetric Reduction Ansatz” holds.


Semi-Infinite Programming Optimality condition Reduction Ansatz 

AMS Subject Classification

90C34 90C46 90C31 90C47 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Günzel H.: The structured jet transversality theorem. Optimization 57, 159–164 (2008)CrossRefGoogle Scholar
  2. 2.
    Günzel H., Jongen H.Th., Stein O.: On the closure of the feasible set in Generalized Semi-Infinite Programming. CEJOR 15, 271–280 (2007)CrossRefGoogle Scholar
  3. 3.
    Günzel, H., Jongen, H.Th., Stein, O.: Generalized semi-infinite programming: the Symmetric Reduction Ansatz. Optim. Lett. (to appear)Google Scholar
  4. 4.
    Hettich R., Kortanek K.O.: Semi-infinite programming: theory, methods, and applications. SIAM Rev. 35, 380–429 (1993)CrossRefGoogle Scholar
  5. 5.
    Hettich R., Zencke P.: Numerische Methoden der Approximation und semi-infiniten Optimierung. Teubner, Stuttgart (1982)Google Scholar
  6. 6.
    Hoffmann, A., Reinhardt, R.: On reverse Chebyshev Approximation Problems. Technical University of Ilmenau, Preprint No. M08/94 (1994)Google Scholar
  7. 7.
    Jongen H.Th., Jonker P., Twilt F.: Nonlinear Optimization in Finite Dimensions. Kluwer, Dordrecht (2000)Google Scholar
  8. 8.
    Jongen H.Th., Rückmann J.-J.: One-parameter families of feasible sets in semi-infinite optimization. J. Glob. Optim. 14, 181–203 (1999)CrossRefGoogle Scholar
  9. 9.
    Kaplan, A., Tichatschke, R.: On a class of terminal variational problems. In: Guddat, J., Jongen, H.Th., Nožička, F., Still, G., Twilt F. (eds.), Parametric Optimization and Related Topics IV, Peter Lang, Frankfurt a.M., pp. 185–199 (1997)Google Scholar
  10. 10.
    Stein O.: Bi-level Strategies in Semi-infinite Programming. Kluwer, Boston (2003)Google Scholar

Copyright information

© Springer Science+Business Media, LLC. 2008

Authors and Affiliations

  • Harald Günzel
    • 1
  • Hubertus Th. Jongen
    • 1
  • Oliver Stein
    • 2
  1. 1.Department of MathematicsRWTH-Aachen UniversityAachenGermany
  2. 2.Department of EconomicsUniversity of KarlsruheKarlsruheGermany

Personalised recommendations