IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v132y2007i1d10.1007_s10957-006-9082-z.html
   My bibliography  Save this article

General Robust-Optimization Formulation for Nonlinear Programming

Author

Listed:
  • Y. Zhang

    (Rice University)

Abstract

Most research in robust optimization has been focused so far on inequality-only, convex conic programming with simple linear models for the uncertain parameters. Many practical optimization problems, however, are nonlinear and nonconvex. Even in linear programming, the coefficients may still be nonlinear functions of the uncertain parameters. In this paper, we propose robust formulations that extend the robust-optimization approach to a general nonlinear programming setting with parameter uncertainty involving both equality and inequality constraints. The proposed robust formulations are valid in a neighborhood of a given nominal parameter value and are robust to the first-order, thus suitable for applications where reasonable parameter estimations are available and uncertain variations are moderate.

Suggested Citation

  • Y. Zhang, 2007. "General Robust-Optimization Formulation for Nonlinear Programming," Journal of Optimization Theory and Applications, Springer, vol. 132(1), pages 111-124, January.
    • Handle: RePEc:spr:joptap:v:132:y:2007:i:1:d:10.1007_s10957-006-9082-z
    DOI: 10.1007/s10957-006-9082-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-006-9082-z
    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/s10957-006-9082-z?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. Laurent El Ghaoui & Maksim Oks & Francois Oustry, 2003. "Worst-Case Value-At-Risk and Robust Portfolio Optimization: A Conic Programming Approach," Operations Research, INFORMS, vol. 51(4), pages 543-556, August.
    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. Gabrel, Virginie & Murat, Cécile & Thiele, Aurélie, 2014. "Recent advances in robust optimization: An overview," European Journal of Operational Research, Elsevier, vol. 235(3), pages 471-483.
    2. Alabi, Tobi Michael & Lu, Lin & Yang, Zaiyue, 2021. "Stochastic optimal planning scheme of a zero-carbon multi-energy system (ZC-MES) considering the uncertainties of individual energy demand and renewable resources: An integrated chance-constrained and," Energy, Elsevier, vol. 232(C).
    3. C. Cromvik & M. Patriksson, 2010. "On the Robustness of Global Optima and Stationary Solutions to Stochastic Mathematical Programs with Equilibrium Constraints, Part 1: Theory," Journal of Optimization Theory and Applications, Springer, vol. 144(3), pages 461-478, March.
    4. Emilio Carrizosa & Frédéric Messine, 2021. "An interval branch and bound method for global Robust optimization," Journal of Global Optimization, Springer, vol. 80(3), pages 507-522, July.
    5. E. T. Hale & Y. Zhang, 2007. "Case Studies for a First-Order Robust Nonlinear Programming Formulation," Journal of Optimization Theory and Applications, Springer, vol. 134(1), pages 27-45, July.
    6. Hsien-Chung Wu, 2019. "Numerical Method for Solving the Robust Continuous-Time Linear Programming Problems," Mathematics, MDPI, vol. 7(5), pages 1-50, May.
    7. Hsien-Chung Wu, 2021. "Robust Solutions for Uncertain Continuous-Time Linear Programming Problems with Time-Dependent Matrices," Mathematics, MDPI, vol. 9(8), pages 1-52, April.
    8. Soleimanian, Azam & Salmani Jajaei, Ghasemali, 2013. "Robust nonlinear optimization with conic representable uncertainty set," European Journal of Operational Research, Elsevier, vol. 228(2), pages 337-344.
    9. Theodor Komann & Michael Wiesheu & Stefan Ulbrich & Sebastian Schöps, 2024. "Robust Design Optimization of Electric Machines with Isogeometric Analysis," Mathematics, MDPI, vol. 12(9), pages 1-18, April.
    10. Dimitris Bertsimas & Omid Nohadani & Kwong Meng Teo, 2010. "Robust Optimization for Unconstrained Simulation-Based Problems," Operations Research, INFORMS, vol. 58(1), pages 161-178, February.

    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. 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.
    2. Cui, Xueting & Zhu, Shushang & Sun, Xiaoling & Li, Duan, 2013. "Nonlinear portfolio selection using approximate parametric Value-at-Risk," Journal of Banking & Finance, Elsevier, vol. 37(6), pages 2124-2139.
    3. Barrieu, Pauline & Scandolo, Giacomo, 2014. "Assessing financial model risk," LSE Research Online Documents on Economics 60084, London School of Economics and Political Science, LSE Library.
    4. Humphery-Jenner, M., 2011. "Anti-takeover Provisions as a Source of Innovation and Value Creation," Discussion Paper 2011-045, Tilburg University, Center for Economic Research.
    5. Steve Zymler & Daniel Kuhn & Berç Rustem, 2013. "Worst-Case Value at Risk of Nonlinear Portfolios," Management Science, INFORMS, vol. 59(1), pages 172-188, July.
    6. Walid Ben-Ameur & Adam Ouorou & Guanglei Wang & Mateusz Żotkiewicz, 2018. "Multipolar robust optimization," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(4), pages 395-434, December.
    7. Mainik, Georg & Mitov, Georgi & Rüschendorf, Ludger, 2015. "Portfolio optimization for heavy-tailed assets: Extreme Risk Index vs. Markowitz," Journal of Empirical Finance, Elsevier, vol. 32(C), pages 115-134.
    8. Asimit, Alexandru V. & Bignozzi, Valeria & Cheung, Ka Chun & Hu, Junlei & Kim, Eun-Seok, 2017. "Robust and Pareto optimality of insurance contracts," European Journal of Operational Research, Elsevier, vol. 262(2), pages 720-732.
    9. Maillet, Bertrand & Tokpavi, Sessi & Vaucher, Benoit, 2015. "Global minimum variance portfolio optimisation under some model risk: A robust regression-based approach," European Journal of Operational Research, Elsevier, vol. 244(1), pages 289-299.
    10. L. Jeff Hong & Zhiyuan Huang & Henry Lam, 2021. "Learning-Based Robust Optimization: Procedures and Statistical Guarantees," Management Science, INFORMS, vol. 67(6), pages 3447-3467, June.
    11. Jang Ho Kim & Woo Chang Kim & Frank J. Fabozzi, 2017. "Penalizing variances for higher dependency on factors," Quantitative Finance, Taylor & Francis Journals, vol. 17(4), pages 479-489, April.
    12. Ximing Wang & Neng Fan & Panos M. Pardalos, 2018. "Robust chance-constrained support vector machines with second-order moment information," Annals of Operations Research, Springer, vol. 263(1), pages 45-68, April.
    13. Maria Scutellà & Raffaella Recchia, 2013. "Robust portfolio asset allocation and risk measures," Annals of Operations Research, Springer, vol. 204(1), pages 145-169, April.
    14. Onur Babat & Juan C. Vera & Luis F. Zuluaga, 2021. "Computing near-optimal Value-at-Risk portfolios using Integer Programming techniques," Papers 2107.07339, arXiv.org.
    15. Bazovkin, Pavel, 2014. "Geometrical framework for robust portfolio optimization," Discussion Papers in Econometrics and Statistics 01/14, University of Cologne, Institute of Econometrics and Statistics.
    16. Scholz, Roland W. & Czichos, Reiner & Parycek, Peter & Lampoltshammer, Thomas J., 2020. "Organizational vulnerability of digital threats: A first validation of an assessment method," European Journal of Operational Research, Elsevier, vol. 282(2), pages 627-643.
    17. Barrieu, Pauline & Scandolo, Giacomo, 2015. "Assessing financial model risk," European Journal of Operational Research, Elsevier, vol. 242(2), pages 546-556.
    18. Kolm, Petter N. & Tütüncü, Reha & Fabozzi, Frank J., 2014. "60 Years of portfolio optimization: Practical challenges and current trends," European Journal of Operational Research, Elsevier, vol. 234(2), pages 356-371.
    19. Zhi Chen & Melvyn Sim & Peng Xiong, 2020. "Robust Stochastic Optimization Made Easy with RSOME," Management Science, INFORMS, vol. 66(8), pages 3329-3339, August.
    20. Costa, Oswaldo L.V. & de Oliveira Ribeiro, Celma & Rego, Erik Eduardo & Stern, Julio Michael & Parente, Virginia & Kileber, Solange, 2017. "Robust portfolio optimization for electricity planning: An application based on the Brazilian electricity mix," Energy Economics, Elsevier, vol. 64(C), pages 158-169.

    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:joptap:v:132:y:2007:i:1:d:10.1007_s10957-006-9082-z. 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.