A lifting method for generalized semi-infinite programs based on lower level Wolfe duality
AbstractThis paper introduces novel numerical solution strategies for generalized semi-infinite optimization problems (GSIP), a class of mathematical optimization problems which occur naturally in the context of design centering problems, robust optimization problems, and many fields of engineering science. GSIPs can be regarded as bilevel optimization problems, where a parametric lower-level maximization problem has to be solved in order to check feasibility of the upper level minimization problem. The current paper discusses several strategies to reformulate this class of problems into equivalent finite minimization problems by exploiting the concept of Wolfe duality for convex lower level problems. Here, the main contribution is the discussion of the non-degeneracy of the corresponding formulations under various assumptions. Finally, these non-degenerate reformulations of the original GSIP allow us to apply standard nonlinear optimization algorithms. Copyright Springer Science+Business Media, LLC 2013
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoArticle provided by Springer in its journal Computational Optimization and Applications.
Volume (Year): 54 (2013)
Issue (Month): 1 (January)
Contact details of provider:
Web page: http://www.springer.com/math/journal/10589
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Harald Günzel & Hubertus Jongen & Oliver Stein, 2007. "On the closure of the feasible set in generalized semi-infinite programming," Central European Journal of Operations Research, Springer, vol. 15(3), pages 271-280, September.
- Gerhard-Wilhelm Weber & Aysun Tezel, 2007. "On generalized semi-infinite optimization of genetic networks," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 15(1), pages 65-77, July.
- Stein, Oliver, 2012. "How to solve a semi-infinite optimization problem," European Journal of Operational Research, Elsevier, vol. 223(2), pages 312-320.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Guenther Eichhorn) or (Christopher F Baum).
If references are entirely missing, you can add them using this form.