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

Bärmann A, Heidt A, Martin A, Pokutta S, Thurner C (2015)


Publication Language: English

Publication Type: Journal article

Publication year: 2015

Journal

Publisher: Springer Verlag

Book Volume: 13

Pages Range: 151-193

Journal Issue: 2

DOI: 10.1007/s10287-015-0243-0

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.

Authors with CRIS profile

Involved external institutions

How to cite

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: Download