Polyhedral approximation of ellipsoidal uncertainty sets via extended formulations: a computational case study
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- Bärmann, A., Heidt, A., Martin, A. et al. Comput Manag Sci (2016) 13: 151. doi:10.1007/s10287-015-0243-0
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.