Robust duality analysis for efficiency via convexificators in nonsmooth nonconvex single - objective optimization problems
Nội dung chính của bài viết
Tóm tắt
In this paper, we explore robust duality results between the primal nonsmooth nonconvex single-objective optimization problem with uncertain data (UNMP) and its Mond-Weir-type dual model (DUNMP) in terms of ϵ-upper convexificators: weak ϵ-duality theorem, strong ϵ-duality theorem and converse ϵ-duality theorem, where ϵ ≥ 0.
Từ khóa
Uncertain data, Mond-Weir-type dual problem, ϵ−duality theorems
Chi tiết bài viết
Tài liệu tham khảo
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[5] Chuong T.D.: Robust optimality and duality in multiobjective optimization problems under data uncertainty. SIAM J Optim. 30(2), 1501–1526 (2020)
[6] Chen J. W., Yanga R., K¨obis E., and Ou X.: Convexificators for nonconvex multiobjective optimization problems with uncertain data: robust optimality and duality. Optimization (online), 1–23 (2023)
[7] Chen J., K¨obis E., and Yao JC.: Optimality conditions and duality for robust nonsmooth multiobjective optimization problems with constraints. J. Optim. Theory Appl. 181, 411–436 (2019)
[8] Jeyakumar V., Luc D.T.: Nonsmooth calculus, minimality, and monotonicity of convexificators. J. Optim. Theory. Appl. 101, 599–621 (1999)
[9] Loridan, P.: ϵ−solutions in vector minimization problems. J. Optim. Theory Appl. 43, 265–276 (1984)
[10] Luu D.V.: Optimality conditions for local efficient solutions of vector equilibrium problems via convexificators and applications. J. Optim. Theory. Appl. 171, 643–665 (2016)
[11] Luu D.V.: Necessary and sufficient conditions for efficiency via convexificators. J. Optim. Theory Appl. 160, 510–526 (2014)
[12] Luu D.V.: Necessary efficiency conditions for vector equilibrium problems with general inequality constraints via convexificators. Bull. Braz. Math. Soc. New Series. 50, 685–704 (2019)
[13] Hong, Z., Bae, K.D., Kim, D.S.: Minimax programming as a tool for studying robust multi-objective optimization problems. Ann. Oper. Res. 319, 1589–1606 (2022)
[14] Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)
[15] Su T.V.: Robust nonsmooth optimality conditions for uncertain multiobjective programs involving stable functions. Positivity. 28: 60 (2024) DOI: https://doi.org/10.1007/s11117-024-01077-w
[16] Su T.V.: Optimality analysis for ϵ−quasi solutions of optimization problems via ϵ−upper convexificators: a dual approach. J. Global Optim. 90, 651–669 (2024) DOI: https://doi.org/10.1007/s10898-024-01415-y
[17] Thuy N.T.T., Su T.V., Linh D.H.: Robust optimality conditions for multiobjective programming problems under data uncertainty and its applications. Optimization. 73 (3), 641–672 (2024)
[2] Clarke, F.H.: Optimization and Nonsmooth Analysis. WileyInterscience, New York (1983)
[3] Capˆatˆa, A.: Optimality conditions for ϵ−quasi solutions of optimization problems via ϵ−upper convexificators with applications. Optim. Lett. 13, 857–873 (2019)
[4] Chen J.W., Yang R., K¨obis E., Ou X.: Convexificators for nonconvex multiobjective optimization problems with uncertain data: robust optimality and duality. Optimization. (2023); DOI: https://doi.org/10.1080/02331934.2023.229361
[5] Chuong T.D.: Robust optimality and duality in multiobjective optimization problems under data uncertainty. SIAM J Optim. 30(2), 1501–1526 (2020)
[6] Chen J. W., Yanga R., K¨obis E., and Ou X.: Convexificators for nonconvex multiobjective optimization problems with uncertain data: robust optimality and duality. Optimization (online), 1–23 (2023)
[7] Chen J., K¨obis E., and Yao JC.: Optimality conditions and duality for robust nonsmooth multiobjective optimization problems with constraints. J. Optim. Theory Appl. 181, 411–436 (2019)
[8] Jeyakumar V., Luc D.T.: Nonsmooth calculus, minimality, and monotonicity of convexificators. J. Optim. Theory. Appl. 101, 599–621 (1999)
[9] Loridan, P.: ϵ−solutions in vector minimization problems. J. Optim. Theory Appl. 43, 265–276 (1984)
[10] Luu D.V.: Optimality conditions for local efficient solutions of vector equilibrium problems via convexificators and applications. J. Optim. Theory. Appl. 171, 643–665 (2016)
[11] Luu D.V.: Necessary and sufficient conditions for efficiency via convexificators. J. Optim. Theory Appl. 160, 510–526 (2014)
[12] Luu D.V.: Necessary efficiency conditions for vector equilibrium problems with general inequality constraints via convexificators. Bull. Braz. Math. Soc. New Series. 50, 685–704 (2019)
[13] Hong, Z., Bae, K.D., Kim, D.S.: Minimax programming as a tool for studying robust multi-objective optimization problems. Ann. Oper. Res. 319, 1589–1606 (2022)
[14] Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)
[15] Su T.V.: Robust nonsmooth optimality conditions for uncertain multiobjective programs involving stable functions. Positivity. 28: 60 (2024) DOI: https://doi.org/10.1007/s11117-024-01077-w
[16] Su T.V.: Optimality analysis for ϵ−quasi solutions of optimization problems via ϵ−upper convexificators: a dual approach. J. Global Optim. 90, 651–669 (2024) DOI: https://doi.org/10.1007/s10898-024-01415-y
[17] Thuy N.T.T., Su T.V., Linh D.H.: Robust optimality conditions for multiobjective programming problems under data uncertainty and its applications. Optimization. 73 (3), 641–672 (2024)