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

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  • 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
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    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. 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.
    12. 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.
    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. 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.
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    1. T. D. Chuong & V. Jeyakumar, 2025. "Adjustable robust multiobjective linear optimization: Pareto optimal solutions via conic programming," Annals of Operations Research, Springer, vol. 346(2), pages 895-916, March.
    2. Holger Berthold & Till Heller & Tobias Seidel, 2024. "A unified approach to inverse robust optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 99(1), pages 115-139, April.
    3. 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.
    4. 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.

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