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

Author

Listed:
  • Andreas Bärmann

    (FAU Erlangen-Nürnberg)

  • Andreas Heidt

    (FAU Erlangen-Nürnberg)

  • Alexander Martin

    (FAU Erlangen-Nürnberg)

  • Sebastian Pokutta

    (Georgia Institute of Technology)

  • Christoph Thurner

    (FAU Erlangen-Nürnberg)

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.

Suggested Citation

  • Andreas Bärmann & Andreas Heidt & Alexander Martin & Sebastian Pokutta & Christoph Thurner, 2016. "Polyhedral approximation of ellipsoidal uncertainty sets via extended formulations: a computational case study," Computational Management Science, Springer, vol. 13(2), pages 151-193, April.
    • Handle: RePEc:spr:comgts:v:13:y:2016:i:2:d:10.1007_s10287-015-0243-0
    DOI: 10.1007/s10287-015-0243-0
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    References listed on IDEAS

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    1. Juan Pablo Vielma & Shabbir Ahmed & George L. Nemhauser, 2008. "A Lifted Linear Programming Branch-and-Bound Algorithm for Mixed-Integer Conic Quadratic Programs," INFORMS Journal on Computing, INFORMS, vol. 20(3), pages 438-450, August.
    2. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    3. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    4. Aharon Ben-Tal & Arkadi Nemirovski, 2001. "On Polyhedral Approximations of the Second-Order Cone," Mathematics of Operations Research, INFORMS, vol. 26(2), pages 193-205, May.
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    Cited by:

    1. Andreas Bärmann & Andreas Heidt & Alexander Martin & Sebastian Pokutta & Christoph Thurner, 2017. "Erratum to: Polyhedral approximation of ellipsoidal uncertainty sets via extended formulations: a computational case study," Computational Management Science, Springer, vol. 14(2), pages 293-296, April.

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