Điều kiện tối ưu và đối ngẫu cho bài toán tối ưu nửa vô hạn dạng phân số với dữ liệu không chắc chắn sử dụng dưới vi phân Mordukhovich
Abstract
In this paper, optimality conditions and duality theorems for a positively properly efficient solution of a nonsmooth fractional semi-infinite optimization problem with data uncertainty in the constraints are studied via Mordukhovich subdifferential. Some examples are given to illustrate the obtained results.
Tóm tắt
Trong bài viết này, điều kiện tối ưu và các định lý đối ngẫu cho nghiệm chính thường của bài toán tối ưu nửa vô hạn không trơn dạng phân số với dữ liệu không chắc chắn trong những ràng buộc được nghiên cứu thông qua dưới vi phân Mordukhovich. Kết quả đạt được của nghiên cứu được chứng minh thông qua những ví dụ minh họa cụ thể.
Article Details
Tài liệu tham khảo
Chen, J. W., Kobis, E. & Yao, J. C. (2019). Optimality conditions and duality for robust nonsmooth multiobjective optimization problems with constraints. Journal of Optimization Theory and Applications, 181, 411 - 436. https://doi.org/10.1007/s10957-018-1437-8
Chuong, T. D. (2013). Optimality and duality for proper and isolated efficiencies in multiobjective optimization. Nonlinear Analysis 76, 93 - 104. https://doi.org/10.1016/j.na.2012.08.005
Chuong, T. D., & Kim, D. S. (2014). Nonsmooth semi-infinite multiobjective optimization problems. Journal of Optimization Theory and Applications 160, 748 - 762. https://doi.org/10.1007/s10957-013-0314-8
Chuong, T. D., & Yao, J. C. (2014). Isolated and proper efficiencies in semi-infinite vector optimization problems. Journal of Optimization Theory and Applications 162, 447 - 462 (2014). https://doi.org/10.1007/s10957-013-0425-2
Chuong, T. D. (2016). Optimality and duality for robust multiobjective optimization problems. Nonlinear Analysis, 134, 127 - 143. https://doi.org/10.1016/j.na.2016.01.002
Chuong, T. D. (2016). Nondifferentiable fractional semi-infinite multiobjective optimization problems. Operations Research Letters, 44, 260 - 266. https://doi.org/10.1016/j.orl.2016.02.003
Chuong, T. D. (2020). Robust optimality and duality in multiobjective optimization problems under data uncertainty. SIAM Journal on Optimization, 30, 1501 - 1526. https://doi.org/10.1137/19M1251461
Dinh, N., Goberna, M. A., Lopez, M. A., & Volle, M. A. (2017). unifying approach to robust convex infinite optimization duality. Journal of Optimization Theory and Applications, 174, 650 - 685. https://doi.org/10.1007/s10957-017-1136-x
Dinh, N., Long, D. H., & Yao, J. C. (2020). Duality for Robust Linear In nite Programming Problems Revisited. Vietnam Journal of Mathematics, 46, 293 - 328. https://doi.org/10.1007/s10013-018-0283-1
Fakhar, M., Mahyarinia, M. R., & Zafarani, J. (2018). On nonsmooth robust multiobjective optimization under generalized convexity with applications to portfolio optimization. European Journal of Operational Research, 265, 39 - 48. https://doi.org/10.1016/j.ejor.2017.08.003
Fakhara, M., Mahyarinia, M. R., & Zafarani, J. (2019). On approximate solutions for nonsmooth robust multiobjective optimization problems. Optimization, 68, 1653 - 1683. https://doi.org/10.1080/02331934.2019.1579212
Khanh, P. Q., & Tung, N. M. (2020). On the Mangasarian - Fromovitz constraint qualification and Karush - Kuhn - Tucker conditions in nonsmooth semi-infinite multiobjective programming. Optimization Letters, 14, 2055-2072. https://doi.org/10.1007/s11590-019-01529-3
Khantree, C., & Wangkeeree, R. (2019). On quasi approximate solutions for nonsmooth robust semi-infinite optimization problems. Carpathian Journal of Mathematics, 35, 417 - 426. https://doi.org/10.37193/CJM.2019.03.16
Mordukhovich, B. S. (2006). Variational Analysis and Generalized Differentiation. I: Basic Theory. Springer, Berlin. https://doi.org/10.1007/3-540-31247-1
Singh, V., Jayswal, A., Stancu-Minasian, I. & Rusu-Stancu, A. M. (2021). Isolated and proper efficiencies for semi-infinite multiobjective fractional problems. Series A Applied Mathematics and Physics, 83, 111 - 124.
Son, T. Q., Tuyen, N. V., & Wen, C. F. (2020). Optimality conditions for approximate Pareto solutions of a nonsmooth vector optimization problem with an infinite number of constraints. Acta Mathematica Vietnamica, 45, 435 - 448. https://doi.org/10.1007/s40306-019-00358-x
Sun, X. K., Teo, K. L., Zheng, J., & Liu, L. (2020). Robust approximate optimal solutions for nonlinear semi-infinite programming with uncertainty. Optimization, 69, 2109 - 2129. https://doi.org/10.1080/02331934.2020.1763990
Tung, L. T. (2020). Karush - Kuhn - Tucker optimality conditions and duality for multiobjective semi-infinite programming via tangential subdifferentials. Numerical Functional Analysis and Optimization, 41, 659 - 684. https://doi.org/10.1080/01630563.2019.1667826
Tung, L. T. (2021). Strong Karush - Kuhn - Tucker optimality conditions for Borwein properly efficient solutions of multiobjective semi-infinite programming. Bulletin of the Brazilian Mathematical Society, 52, 1 - 22. https://doi.org/10.1007/s00574-019-00190-9