Abstract
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.
Similar content being viewed by others
References
Günzel H.: The structured jet transversality theorem. Optimization 57, 159–164 (2008)
Günzel H., Jongen H.Th., Stein O.: On the closure of the feasible set in Generalized Semi-Infinite Programming. CEJOR 15, 271–280 (2007)
Günzel, H., Jongen, H.Th., Stein, O.: Generalized semi-infinite programming: the Symmetric Reduction Ansatz. Optim. Lett. (to appear)
Hettich R., Kortanek K.O.: Semi-infinite programming: theory, methods, and applications. SIAM Rev. 35, 380–429 (1993)
Hettich R., Zencke P.: Numerische Methoden der Approximation und semi-infiniten Optimierung. Teubner, Stuttgart (1982)
Hoffmann, A., Reinhardt, R.: On reverse Chebyshev Approximation Problems. Technical University of Ilmenau, Preprint No. M08/94 (1994)
Jongen H.Th., Jonker P., Twilt F.: Nonlinear Optimization in Finite Dimensions. Kluwer, Dordrecht (2000)
Jongen H.Th., Rückmann J.-J.: One-parameter families of feasible sets in semi-infinite optimization. J. Glob. Optim. 14, 181–203 (1999)
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)
Stein O.: Bi-level Strategies in Semi-infinite Programming. Kluwer, Boston (2003)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Günzel, H., Jongen, H.T. & Stein, O. Generalized Semi-Infinite Programming: on generic local minimizers. J Glob Optim 42, 413–421 (2008). https://doi.org/10.1007/s10898-008-9302-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10898-008-9302-1