IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v296y2022i3p749-763.html
   My bibliography  Save this article

The radius of robust feasibility of uncertain mathematical programs: A Survey and recent developments

Author

Listed:
  • Goberna, M.A.
  • Jeyakumar, V.
  • Li, G.
  • Vicente-Pérez, J.

Abstract

The radius of robust feasibility provides a numerical value for the largest possible uncertainty set that guarantees feasibility of a robust counterpart of a mathematical program with uncertain constraints. The objective of this review of the state-of-the-art in this field is to present this useful tool of robust optimization to its potential users and to avoid undesirable overlapping of research works on the topic as those we have recently detected. In this paper we overview the existing literature on the radius of robust feasibility in continuous and mixed-integer linearly constrained programs, linearly constrained semi-infinite programs, convexly constrained programs, and conic linearly constrained programs. We also analyze the connection between the radius of robust feasibility and the distance to ill-posedness for different types of uncertain mathematical programs.

Suggested Citation

  • Goberna, M.A. & Jeyakumar, V. & Li, G. & Vicente-Pérez, J., 2022. "The radius of robust feasibility of uncertain mathematical programs: A Survey and recent developments," European Journal of Operational Research, Elsevier, vol. 296(3), pages 749-763.
    • Handle: RePEc:eee:ejores:v:296:y:2022:i:3:p:749-763
    DOI: 10.1016/j.ejor.2021.04.035
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221721003659
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2021.04.035?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. Feng Guo & Xiaoxia Sun, 2020. "On semi-infinite systems of convex polynomial inequalities and polynomial optimization problems," Computational Optimization and Applications, Springer, vol. 75(3), pages 669-699, April.
    2. Sanjay Mehrotra & David Papp, 2013. "A cutting surface algorithm for semi-infinite convex programming with an application to moment robust optimization," Papers 1306.3437, arXiv.org, revised Aug 2014.
    3. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    4. Jiawei Chen & Jun Li & Xiaobing Li & Yibing Lv & Jen-Chih Yao, 2020. "Radius of Robust Feasibility of System of Convex Inequalities with Uncertain Data," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 384-399, February.
    5. M. A. Goberna & V. Jeyakumar & G. Li, 2021. "Calculating Radius of Robust Feasibility of Uncertain Linear Conic Programs via Semi-definite Programs," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 597-622, May.
    6. T. D. Chuong & V. Jeyakumar, 2017. "An Exact Formula for Radius of Robust Feasibility of Uncertain Linear Programs," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 203-226, April.
    7. Goberna, M.A. & Jeyakumar, V. & Li, G. & Vicente-Pérez, J., 2018. "Guaranteeing highly robust weakly efficient solutions for uncertain multi-objective convex programs," European Journal of Operational Research, Elsevier, vol. 270(1), pages 40-50.
    8. N. E. Mastorakis, 2000. "Optimum Radius of Robust Stability for Schur Polynomials," Journal of Optimization Theory and Applications, Springer, vol. 104(1), pages 165-174, January.
    9. Li-Ping Pang & Jian Lv & Jin-He Wang, 2016. "Constrained incremental bundle method with partial inexact oracle for nonsmooth convex semi-infinite programming problems," Computational Optimization and Applications, Springer, vol. 64(2), pages 433-465, June.
    10. Goberna, M.A. & Jeyakumar, V. & Li, G. & Vicente-Pérez, J., 2015. "Robust solutions to multi-objective linear programs with uncertain data," European Journal of Operational Research, Elsevier, vol. 242(3), pages 730-743.
    11. M. J. Cánovas & M. A. López & J. Parra & F. J. Toledo, 2006. "Distance to Ill-Posedness in Linear Optimization via the Fenchel-Legendre Conjugate," Journal of Optimization Theory and Applications, Springer, vol. 130(2), pages 173-183, August.
    12. M. A. Goberna & M. A. López, 2018. "Recent contributions to linear semi-infinite optimization: an update," Annals of Operations Research, Springer, vol. 271(1), pages 237-278, December.
    13. Dimitris Bertsimas & David B. Brown, 2009. "Constructing Uncertainty Sets for Robust Linear Optimization," Operations Research, INFORMS, vol. 57(6), pages 1483-1495, December.
    14. Lars Schewe & Martin Schmidt & Johannes Thürauf, 2020. "Structural properties of feasible bookings in the European entry–exit gas market system," 4OR, Springer, vol. 18(2), pages 197-218, June.
    15. Emilio Carrizosa & Stefan Nickel, 2003. "Robust facility location," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(2), pages 331-349, November.
    16. Younseok Choo, 2014. "Improved Optimum Radius for Robust Stability of Schur Polynomials," Journal of Optimization Theory and Applications, Springer, vol. 161(2), pages 553-556, May.
    17. A. Auslender & A. Ferrer & M. Goberna & M. López, 2015. "Comparative study of RPSALG algorithm for convex semi-infinite programming," Computational Optimization and Applications, Springer, vol. 60(1), pages 59-87, January.
    18. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    19. L.X. Gao & Y.X. Sun, 2002. "On the Optimum Radius of Robust Stability for Schur Polynomials," Journal of Optimization Theory and Applications, Springer, vol. 114(2), pages 471-475, 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. Thai Doan Chuong & Xinghuo Yu & Chen Liu & Andrew Eberhard & Chaojie Li, 2024. "Solving Two-stage Quadratic Multiobjective Problems via Optimality and Relaxations," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 676-713, October.
    2. Miguel A. Goberna & Vaithilingam Jeyakumar & Guoyin Li, 2024. "The Stability of Robustness for Conic Linear Programs with Uncertain Data," Journal of Optimization Theory and Applications, Springer, vol. 203(2), pages 1509-1530, November.

    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. Frauke Liers & Lars Schewe & Johannes Thürauf, 2022. "Radius of Robust Feasibility for Mixed-Integer Problems," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 243-261, January.
    2. M. A. Goberna & V. Jeyakumar & G. Li, 2021. "Calculating Radius of Robust Feasibility of Uncertain Linear Conic Programs via Semi-definite Programs," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 597-622, May.
    3. Groetzner, Patrick & Werner, Ralf, 2022. "Multiobjective optimization under uncertainty: A multiobjective robust (relative) regret approach," European Journal of Operational Research, Elsevier, vol. 296(1), pages 101-115.
    4. M. A. Goberna & M. A. López, 2018. "Recent contributions to linear semi-infinite optimization: an update," Annals of Operations Research, Springer, vol. 271(1), pages 237-278, December.
    5. Bo Wei & William B. Haskell & Sixiang Zhao, 2020. "The CoMirror algorithm with random constraint sampling for convex semi-infinite programming," Annals of Operations Research, Springer, vol. 295(2), pages 809-841, December.
    6. 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.
    7. Chassein, André & Goerigk, Marc, 2018. "Variable-sized uncertainty and inverse problems in robust optimization," European Journal of Operational Research, Elsevier, vol. 264(1), pages 17-28.
    8. Claire Nicolas & Stéphane Tchung-Ming & Emmanuel Hache, 2016. "Energy transition in transportation under cost uncertainty, an assessment based on robust optimization," Working Papers hal-02475943, HAL.
    9. Knoke, Thomas & Paul, Carola & Härtl, Fabian & Castro, Luz Maria & Calvas, Baltazar & Hildebrandt, Patrick, 2015. "Optimizing agricultural land-use portfolios with scarce data—A non-stochastic model," Ecological Economics, Elsevier, vol. 120(C), pages 250-259.
    10. Dimitris Bertsimas & Melvyn Sim & Meilin Zhang, 2019. "Adaptive Distributionally Robust Optimization," Management Science, INFORMS, vol. 65(2), pages 604-618, February.
    11. Huan Xu & Constantine Caramanis & Shie Mannor, 2012. "Optimization Under Probabilistic Envelope Constraints," Operations Research, INFORMS, vol. 60(3), pages 682-699, June.
    12. Nikulin, Yury, 2006. "Robustness in combinatorial optimization and scheduling theory: An extended annotated bibliography," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 606, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    13. Fernandes, Betina & Street, Alexandre & Valladão, Davi & Fernandes, Cristiano, 2016. "An adaptive robust portfolio optimization model with loss constraints based on data-driven polyhedral uncertainty sets," European Journal of Operational Research, Elsevier, vol. 255(3), pages 961-970.
    14. Thai Doan Chuong, 2021. "Radius of Robust Global Error Bound for Piecewise Linear Inequality Systems," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 68-82, October.
    15. Fertis, Apostolos & Baes, Michel & Lüthi, Hans-Jakob, 2012. "Robust risk management," European Journal of Operational Research, Elsevier, vol. 222(3), pages 663-672.
    16. Kuhn, K. & Raith, A. & Schmidt, M. & Schöbel, A., 2016. "Bi-objective robust optimisation," European Journal of Operational Research, Elsevier, vol. 252(2), pages 418-431.
    17. Jornada, Daniel & Leon, V. Jorge, 2016. "Biobjective robust optimization over the efficient set for Pareto set reduction," European Journal of Operational Research, Elsevier, vol. 252(2), pages 573-586.
    18. Marla, Lavanya & Rikun, Alexander & Stauffer, Gautier & Pratsini, Eleni, 2020. "Robust modeling and planning: Insights from three industrial applications," Operations Research Perspectives, Elsevier, vol. 7(C).
    19. Sandra Cruz Caçador & Pedro Manuel Cortesão Godinho & Joana Maria Pina Cabral Matos Dias, 2022. "A minimax regret portfolio model based on the investor’s utility loss," Operational Research, Springer, vol. 22(1), pages 449-484, March.
    20. Güray Kara & Ayşe Özmen & Gerhard-Wilhelm Weber, 2019. "Stability advances in robust portfolio optimization under parallelepiped uncertainty," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(1), pages 241-261, March.

    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:eee:ejores:v:296:y:2022:i:3:p:749-763. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.