Computational Management Science

, Volume 13, Issue 2, pp 151–193 | Cite as

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

  • Andreas Bärmann
  • Andreas Heidt
  • Alexander Martin
  • Sebastian Pokutta
  • Christoph Thurner
Original Paper


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.


Robust optimization Approximation Extended formulations Second-order cone optimization Mixed-integer programming Portfolio optimization 

Mathematics Subject Classification

90C31 90C59 90C20 90C11 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Andreas Bärmann
    • 1
  • Andreas Heidt
    • 1
  • Alexander Martin
    • 1
  • Sebastian Pokutta
    • 2
  • Christoph Thurner
    • 1
  1. 1.Lehrstuhl für WirtschaftsmathematikFAU Erlangen-NürnbergErlangenGermany
  2. 2.School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA

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