Robust optimality and duality for bilevel optimization problems under uncertain data

[1] J.F. Bard, Practical Bilevel Optimization: Algorithms and Applications, Springer Science & Business Media, New York, 2013.

[2] Y. Beck, I. Ljubić, and M. Schmidt, A survey on bilevel optimization under uncertainty, European J. Oper. Res. 311 (2023), no. 2, 401–426.  https://doi.org/10.1016/j.ejor.2023.01.008

[3] A. Ben-Tal, L. El Ghaoui, and A. Nemirovski, Robust Optimization, Princeton University Press, Princeton, 2009. https://doi.org/10.1515/9781400831050

[4] J. Chen, E. Köbis, and J.C. Yao, Optimality conditions and duality for robust nonsmooth multiobjective optimization problems with constraints, J. Optim. Theory Appl. 181 (2019), no. 2, 411–436. https://doi.org/10.1007/s10957-018-1437-8

[5] T.D. Chuong, Optimality and duality for robust multiobjective optimization problems, Nonlinear Anal. 134 (2016), 127–143.  https://doi.org/10.1016/j.na.2016.01.002

[6] T.D. Chuong, Optimality conditions for nonsmooth multiobjective bilevel optimization problems, Ann. Oper. Res. 287 (2020), no. 2, 617–642.  https://doi.org/10.1007/s10479-017-2734-6

[7] T.D. Chuong, Robust optimality and duality in multiobjective optimization problems under data uncertainty, SIAM J. Optim. 30 (2020), no. 2, 1501–1526.  https://doi.org/10.1137/19M1251461

[8] F.H. Clarke, Optimization and Nonsmooth Analysis, Society for Industrial and Applied Mathematics, 1990.

[9] S. Dempe, Foundations of Bilevel Programming, Springer Science & Business Media, New York, 2002.

[10] S. Dempe, Annotated bibliography on bilevel programming and mathematical programs with equilibrium constraints, Optimization 52 (2003), no. 3, 333–359.  https://doi.org/10.1080/0233193031000149894

[11] S. Dempe, Bilevel optimization: Theory, algorithms, applications and a bibliography, Bilevel Optimization: Advances and Next Challenges (S. Dempe and A. Zemkoho, eds.), vol. 161, Springer International Publishing, Cham, 2020, pp. 581–672.

[12] S. Dempe and P. Mehlitz, Semivectorial bilevel programming versus scalar bilevel programming, Optimization 69 (2020), no. 4, 657–679. https://doi.org/10.1080/02331934.2019.1625900

[13] N.A. Gadhi, K. Hamdaoui, and M. El idrissi, Sufficient optimality conditions and duality results for a bilevel multiobjective optimization problem via a $\Psi$-reformulation, Optimization 69 (2020), no. 4, 681–702. https://doi.org/10.1080/02331934.2019.1625901

[14] N.A. Gadhi and M. Ohda, Sufficient optimality conditions for a robust multiobjective problem, Asia-Pac. J. Oper. Res. 40 (2023), no. 3, 2250027.  https://doi.org/10.1142/S0217595922500270

[15] N.A. Gadhi and M. Ohda, Applying tangential subdifferentials in bilevel optimization, Optimization 73 (2024), no. 9, 2919–2932.  https://doi.org/10.1080/02331934.2023.2231501

[16] N.A. Gadhi and M. Ohda, Necessary optimality conditions for strictly robust bilevel optimization problems, Optimization (2024), 1–23.  https://doi.org/10.1080/02331934.2024.2370428

[17] J. Goseling and M. Lopuhaä-Zwakenberg, Robust optimization for local differential privacy, 2022 IEEE Int. Sym. Inf. Theory (ISIT) (Espoo, Finland), 2022, pp. 1629–1634.

[18] N.C. Hung, T.D. Chuong, and N.L.H. Anh, Optimality and duality for robust optimization problems involving inters- ection of closed sets, J. Optim. Theory Appl. 202 (2024), no. 2, 771–794.  https://doi.org/10.1007/s10957-024-02447-w

[19] V. Jeyakumar, G. Li, and G.M. Lee, Robust duality for generalized convex programming problems under data uncertainty, Nonlinear Anal. Theory Methods Appl. 75 (2012), no. 3, 1362–1373. https://doi.org/10.1016/j.na.2011.04.006

[20] G.M. Lee and P.T. Son, On nonsmooth optimality theorems for robust optimization problems, Bull. Korean Math. Soc. 51 (2014), no. 1, 287–301.  https://doi.org/10.4134/BKMS.2014.51.1.287

[21] F. Lin, X. Fang, and Z. Gao, Distributionally robust optimization: A review on theory and applications, Numer. Algebra Control Optim. 12 (2022), no. 1, 159–212.  http://dx.doi.org/10.3934/naco.2021057

[22] P. Mehlitz, L.I. Minchenko, and A.B. Zemkoho, A note on partial calmness for bilevel optimization problems with linearly structured lower level, Optim. Lett. 15 (2021), no. 4, 1277–1291. https://doi.org/10.1007/s11590-020-01636-6

[23] J. V. Outrata, On the numerical solution of a class of Stackelberg problems, Zeitschrift für Operations Research 34 (1990), no. 4, 255–277.  https://doi.org/10.1007/BF01416737

[24] A. Ren, Solving the general fuzzy random bilevel programming problem through me measure-based approach, IEEE Access 6 (2018), 25610–25620.  https://doi.org/10.1109/ACCESS.2018.2828706

[25] S. Saini, N. Kailey, and I. Ahmad, Optimality conditions and duality results for a robust bi-level programming problem, RAIRO Oper. Res. 57 (2023), no. 2, 525–539.  https://doi.org/10.1051/ro/2023026

[26] S. Wu and S. Chen, A bi-level algorithm for product line design and pricing, 2014 IEEE International Conference on Industrial Engineering and Engineering Management, 2014, pp. 14–18.

[27] J. Xiao, Y. Cai, Y. He, Y. Xie, and Z. Yang, A dual-randomness bi-level interval multi-objective programming model for regional water resources management, J. Contam. Hydrol. 241 (2021), 103816. https://doi.org/10.1016/j.jconhyd.2021.103816.

[28] J.J. Ye and D.L. Zhu, Optimality conditions for bilevel programming problems, Optimization 33 (1995), no. 1, 9–27. https://doi.org/10.1080/02331939508844060

[29] D. Zhang, H.H. Turan, R. Sarker, and D. Essam, Robust optimization approaches in inventory management: Part A- the survey, IISE Trans. 0 (2024), no. 0, In press.  https://doi.org/10.1080/24725854.2024.2381713

[30] T. Zhang, Z. Chen, Y. Zheng, and J. Chen, An improved simulated annealing algorithm for bilevel multiobjective programming problems with application, J. Nonlinear Sci. Appl. 9 (2016), no. 6, 3672–3685.