Polyhedral approximation of ellipsoidal uncertainty sets via extended formulations: a computational case study

Beitrag in einer Fachzeitschrift


Details zur Publikation

Autor(en): Bärmann A, Heidt A, Martin A, Pokutta S, Thurner C
Zeitschrift: Computational Management Science
Verlag: Springer Verlag
Jahr der Veröffentlichung: 2015
Band: 13
Heftnummer: 2
Seitenbereich: 151-193
ISSN: 1619-697X
eISSN: 1619-6988
Sprache: Englisch


Abstract


Robust optimization is an important technique to immunize optimization problems against data uncertainty. In the case of a linear program and an ellipsoidal uncertainty set, the robust counterpart turns into a second-order cone program. In this work, we investigate the efficiency of linearizing the second-order cone constraints of the latter. This is done using the optimal linear outer-approximation approach by Ben-Tal and Nemirovski (Math Oper Res 26:193--205, 2001) from which we derive an optimal inner approximation of the second-order cone. We examine the performance of this approach on various benchmark sets including portfolio optimization instances as well as (robustified versions of) the MIPLIB and the SNDlib.



FAU-Autoren / FAU-Herausgeber

Bärmann, Andreas Dr.
Lehrstuhl für Wirtschaftsmathematik
Heidt, Andreas
Lehrstuhl für Wirtschaftsmathematik
Martin, Alexander Prof. Dr.
Lehrstuhl für Wirtschaftsmathematik
Thurner, Christoph Dr.
Lehrstuhl für Wirtschaftsmathematik


Autor(en) der externen Einrichtung(en)
Georgia Institute of Technology


Zitierweisen

APA:
Bärmann, A., Heidt, A., Martin, A., Pokutta, S., & Thurner, C. (2015). Polyhedral approximation of ellipsoidal uncertainty sets via extended formulations: a computational case study. Computational Management Science, 13(2), 151-193. https://dx.doi.org/10.1007/s10287-015-0243-0

MLA:
Bärmann, Andreas, et al. "Polyhedral approximation of ellipsoidal uncertainty sets via extended formulations: a computational case study." Computational Management Science 13.2 (2015): 151-193.

BibTeX: 

Zuletzt aktualisiert 2018-12-12 um 13:50