Generalized semi-infinite programming: the Symmetric Reduction Ansatz | Optimization Letters Skip to main content
Springer Nature Link
Log in

Generalized semi-infinite programming: the Symmetric Reduction Ansatz

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

We introduce the Symmetric Reduction Ansatz at a point from the closure of the feasible set in generalized semi-infinite programming. A corresponding Symmetric Reduction Lemma is shown for the local description of the latter set, and optimality conditions as well as topological properties are derived. We conjecture that the Symmetric Reduction Ansatz holds at all local minimizers of generic generalized semi-infinite programs.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Fiacco A.V. and McCormick G.P. (1968). Nonlinear Programming: Sequential Unconstrained Minimization Techniques. Wiley, New York

    MATH  Google Scholar 

  2. Günzel, H., Jongen, H.Th., Stein, O.: On the closure of the feasible set in generalized semi-infinite programming. Cent. Eur. J. Oper. Res. (2007, in press)

  3. Guerra Vázquez, F., Rückmann, J.-J., Stein, O., Still, G.: Generalized semi-infinite programming: a tutorial. J. Comput. Appl. Math. (2007, in press)

  4. Hettich, R., Jongen, H.Th.: Semi-infinite programming: conditions of optimality and applications. In: Stoer, J. (ed.) Optimization Techniques, Part 2, Lecture Notes in Control and Information Sciences, vol. 7, pp. 1–11. Springer, Berlin (1978)

  5. Hettich R. and Still G. (1995). Second order optimality conditions for generalized semi-infinite programming problems. Optimization 34: 195–211

    Article  MATH  MathSciNet  Google Scholar 

  6. Jongen H.Th., Jonker P. and Twilt F. (2000). Nonlinear Optimization in Finite Dimensions. Kluwer, Dordrecht

    MATH  Google Scholar 

  7. Jongen H.Th., Meer K. and Triesch E. (2004). Optimization Theory. Kluwer, Boston

    MATH  Google Scholar 

  8. Stein, O.: On parametric semi-infinite optimization. Thesis, Shaker, Aachen (1997)

  9. Stein O. (2000). On level sets of marginal functions. Optimization 48: 43–67

    Article  MATH  MathSciNet  Google Scholar 

  10. Stein O. (2001). First order optimality conditions for degenerate index sets in generalized semi-infinite programming. Math. Oper. Res. 26: 565–582

    Article  MATH  MathSciNet  Google Scholar 

  11. Stein O. (2003). Bi-level Strategies in Semi-infinite Programming. Kluwer, Boston

    MATH  Google Scholar 

  12. Stein O. (2006). A semi-infinite approach to design centering. In: Dempe, S. and Kalashnikow, S. (eds) Optimization with Multivalued Mappings, pp 209–228. Springer, Heidelberg

    Chapter  Google Scholar 

  13. Stein O. and Still G. (2002). On generalized semi-infinite optimization and bilevel optimization. Eur. J. Oper. Res. 142: 444–462

    Article  MATH  MathSciNet  Google Scholar 

  14. Wetterling W. (1970). Definitheitsbedingungen für relative Extrema bei Optimierungs- und Approximationsaufgaben. Numerische Mathematik 15: 122–136

    Article  MATH  MathSciNet  Google Scholar 

  15. Zwier, G.: Structural analysis in semi-infinite programming. Thesis, University of Twente (1987)

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, RWTH Aachen University, 52056, Aachen, Germany

    H. Günzel & H. Th. Jongen

  2. School of Economics and Business Engineering, University of Karlsruhe, 76128, Karlsruhe, Germany

    O. Stein

Authors
  1. H. Günzel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Th. Jongen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. O. Stein
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to O. Stein.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Günzel, H., Jongen, H.T. & Stein, O. Generalized semi-infinite programming: the Symmetric Reduction Ansatz. Optimization Letters 2, 415–424 (2008). https://doi.org/10.1007/s11590-007-0069-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-007-0069-y

Keywords

Search

Navigation