IDEAS home Printed from https://ideas.repec.org/a/spr/comgts/v13y2016i2d10.1007_s10287-015-0243-0.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10287-015-0243-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10287-015-0243-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    2. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Erfan Mehmanchi & Andrés Gómez & Oleg A. Prokopyev, 2019. "Fractional 0–1 programs: links between mixed-integer linear and conic quadratic formulations," Journal of Global Optimization, Springer, vol. 75(2), pages 273-339, October.
    2. Mohammad R. Oskoorouchi & Hamid R. Ghaffari & Tamás Terlaky & Dionne M. Aleman, 2011. "An Interior Point Constraint Generation Algorithm for Semi-Infinite Optimization with Health-Care Application," Operations Research, INFORMS, vol. 59(5), pages 1184-1197, October.
    3. Alper Atamtürk & Andrés Gómez, 2020. "Submodularity in Conic Quadratic Mixed 0–1 Optimization," Operations Research, INFORMS, vol. 68(2), pages 609-630, March.
    4. Guanglei Wang & Hassan Hijazi, 2018. "Mathematical programming methods for microgrid design and operations: a survey on deterministic and stochastic approaches," Computational Optimization and Applications, Springer, vol. 71(2), pages 553-608, November.
    5. Krokhmal, Pavlo A. & Soberanis, Policarpio, 2010. "Risk optimization with p-order conic constraints: A linear programming approach," European Journal of Operational Research, Elsevier, vol. 201(3), pages 653-671, March.
    6. Alexander Vinel & Pavlo Krokhmal, 2014. "On Valid Inequalities for Mixed Integer p-Order Cone Programming," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 439-456, February.
    7. Gülpınar, Nalan & Pachamanova, Dessislava & Çanakoğlu, Ethem, 2013. "Robust strategies for facility location under uncertainty," European Journal of Operational Research, Elsevier, vol. 225(1), pages 21-35.
    8. Jianwen Ren & Yingqiang Xu & Shiyuan Wang, 2018. "A Distributed Robust Dispatch Approach for Interconnected Systems with a High Proportion of Wind Power Penetration," Energies, MDPI, vol. 11(4), pages 1-18, April.
    9. Wenqing Chen & Melvyn Sim & Jie Sun & Chung-Piaw Teo, 2010. "From CVaR to Uncertainty Set: Implications in Joint Chance-Constrained Optimization," Operations Research, INFORMS, vol. 58(2), pages 470-485, April.
    10. Stefan Mišković, 2017. "A VNS-LP algorithm for the robust dynamic maximal covering location problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(4), pages 1011-1033, October.
    11. Sarhadi, Hassan & Naoum-Sawaya, Joe & Verma, Manish, 2020. "A robust optimization approach to locating and stockpiling marine oil-spill response facilities," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 141(C).
    12. Li, Shukai & Liu, Ronghui & Yang, Lixing & Gao, Ziyou, 2019. "Robust dynamic bus controls considering delay disturbances and passenger demand uncertainty," Transportation Research Part B: Methodological, Elsevier, vol. 123(C), pages 88-109.
    13. Jeong, Jaehee & Premsankar, Gopika & Ghaddar, Bissan & Tarkoma, Sasu, 2024. "A robust optimization approach for placement of applications in edge computing considering latency uncertainty," Omega, Elsevier, vol. 126(C).
    14. Chassein, André & Dokka, Trivikram & Goerigk, Marc, 2019. "Algorithms and uncertainty sets for data-driven robust shortest path problems," European Journal of Operational Research, Elsevier, vol. 274(2), pages 671-686.
    15. Kandpal, Bakul & Pareek, Parikshit & Verma, Ashu, 2022. "A robust day-ahead scheduling strategy for EV charging stations in unbalanced distribution grid," Energy, Elsevier, vol. 249(C).
    16. Guo, Shiliang & Li, Pengpeng & Ma, Kai & Yang, Bo & Yang, Jie, 2022. "Robust energy management for industrial microgrid considering charging and discharging pressure of electric vehicles," Applied Energy, Elsevier, vol. 325(C).
    17. Shen, Feifei & Zhao, Liang & Wang, Meihong & Du, Wenli & Qian, Feng, 2022. "Data-driven adaptive robust optimization for energy systems in ethylene plant under demand uncertainty," Applied Energy, Elsevier, vol. 307(C).
    18. Baringo, Luis & Boffino, Luigi & Oggioni, Giorgia, 2020. "Robust expansion planning of a distribution system with electric vehicles, storage and renewable units," Applied Energy, Elsevier, vol. 265(C).
    19. Barzanjeh, Shakoor & Ahmadizar, Fardin & Arkat, Jamal, 2025. "Logic-based benders decomposition algorithm for robust parallel drone scheduling problem considering uncertain travel times for drones," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 193(C).
    20. Hasani, Aliakbar & Khosrojerdi, Amirhossein, 2016. "Robust global supply chain network design under disruption and uncertainty considering resilience strategies: A parallel memetic algorithm for a real-life case study," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 87(C), pages 20-52.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:comgts:v:13:y:2016:i:2:d:10.1007_s10287-015-0243-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.