多目标区间值优化问题的近似最优性条件
Approximate Optimality Conditions for Multiobjective Interval-Valued Optimization Problems
摘要: 本文考虑带不等式约束的多目标区间值优化问题利用两种序关系分别建立了近似强KKT条件和强互补近似KKT条件。在无任何约束规范的前提下,证明了近似强KKT条件和强互补近似KKT条件的充分和必要条件。
Abstract: This paper addresses multiobjective interval-valued optimization problems subject to inequality constraints. Two types of order relations are adopted to establish the approximate strong KKT conditions and the strong complementary approximate KKT conditions, respectively. In the absence of any constraint qualification, both sufficient and necessary conditions for these approximate KKT conditions are proved.
文章引用:师茗萱, 王海军. 多目标区间值优化问题的近似最优性条件[J]. 运筹与模糊学, 2026, 16(5): 22-32. https://doi.org/10.12677/orf.2026.165031

参考文献

[1] Haeser, G. and Schuverdt, M.L. (2011) On Approximate KKT Condition and Its Extension to Continuous Variational Inequalities. Journal of Optimization Theory and Applications, 149, 528-539.
https://doi.org/10.1007/s10957-011-9802-x
[2] Giorgi, G., Jiménez, B. and Novo, V. (2016) Approximate Karush-Kuhn-Tucker Condition in Multiobjective Optimization. Journal of Optimization Theory and Applications, 171, 70-89.
https://doi.org/10.1007/s10957-016-0986-y
[3] Feng, M. and Li, S. (2018) An Approximate Strong KKT Condition for Multiobjective Optimization. TOP, 26, 489-509.
https://doi.org/10.1007/s11750-018-0491-6
[4] Maurya, J. and Mishra, S. (2022) Strong Complementary Approximate Karush-Kuhn-Tucker Conditions for Multiobjective Optimization Problems. Yugoslav Journal of Operations Research, 32, 219-234.
https://doi.org/10.2298/yjor210315024m
[5] Deng, X., Yang, Y. and Tang, L. (2025) Approximate Karush-Kuhn-Tucker Conditions for Multiobjective Fractional Programming Problems. Journal of Industrial and Management Optimization, 21, 2689-2708.
https://doi.org/10.3934/jimo.2024189
[6] Lv, J., Peng, Z. and Wan, Z. (2024) Approximate Karush-Kuhn-Tucker Condition for Multi-Objective Optimistic Bilevel Programming Problems. Journal of Industrial and Management Optimization, 20, 270-299.
https://doi.org/10.3934/jimo.2023077
[7] Andreani, R., Gómez, W., Haeser, G., Mito, L.M. and Ramos, A. (2022) On Optimality Conditions for Nonlinear Conic Programming. Mathematics of Operations Research, 47, 2160-2185.
https://doi.org/10.1287/moor.2021.1203
[8] Xu, M., Ye, J.J. and Zhang, L. (2015) Smoothing Augmented Lagrangian Method for Nonsmooth Constrained Optimization Problems. Journal of Global Optimization, 62, 675-694.
https://doi.org/10.1007/s10898-014-0242-7
[9] Le, T.T. (2022) Karush-Kuhn-Tucker Optimality Conditions and Duality for Nonsmooth Multiobjective Semi-Infinite Programming Problems with Vanishing Constraints. Applied Set-Valued Analysis and Optimization, 4, 659-684.
[10] Lai, K.K., Maurya, J.K. and Mishra, S.K. (2022) Multiobjective Approximate Gradient Projection Method for Constrained Vector Optimization: Sequential Optimality Conditions without Constraint Qualifications. Journal of Computational and Applied Mathematics, 410, Article 114122.
https://doi.org/10.1016/j.cam.2022.114122
[11] Alefeld, G. and Mayer, G. (2000) Interval Analysis: Theory and Applications. Journal of Computational and Applied Mathematics, 121, 421-464.
https://doi.org/10.1016/s0377-0427(00)00342-3
[12] Ishibuchi, H. and Tanaka, H. (1990) Multiobjective Programming in Optimization of the Interval Objective Function. European Journal of Operational Research, 48, 219-225.
https://doi.org/10.1016/0377-2217(90)90375-l
[13] Wu, H. (2007) The Karush-Kuhn-Tucker Optimality Conditions in an Optimization Problem with Interval-Valued Objective Function. European Journal of Operational Research, 176, 46-59.
https://doi.org/10.1016/j.ejor.2005.09.007
[14] Rani, B.J., Ahmad, I. and Kummari, K. (2023) On Optimality and Duality for Multiobjective Interval-Valued Programming Problems with Vanishing Constraints. Iranian Journal of Numerical Analysis and Optimization, 13, 354-384.
[15] Yadav, T. and Gupta, S.K. (2024) Optimality and Duality Analysis for Multiobjective Interval-Valued Semi-Infinite Optimization Problem Having Vanishing Constraints. Computational and Applied Mathematics, 43, 56-57.
https://doi.org/10.1007/s40314-023-02569-3
[16] Van Su, T. and Hang, D.D. (2022) Optimality Conditions and Duality Theorems for Nonsmooth Semi-Infinite Interval-Valued Mathematical Programs with Vanishing Constraints. Computational and Applied Mathematics, 41, 422-423.
https://doi.org/10.1007/s40314-022-02139-z
[17] Wu, H. (2009) The Karush-Kuhn-Tucker Optimality Conditions in Multiobjective Programming Problems with Interval-Valued Objective Functions. European Journal of Operational Research, 196, 49-60.
https://doi.org/10.1016/j.ejor.2008.03.012
[18] Wu, H. (2009) The Karush-Kuhn-Tucker Optimality Conditions for Multi-Objective Programming Problems with Fuzzy-Valued Objective Functions. Fuzzy Optimization and Decision Making, 8, 1-28.
https://doi.org/10.1007/s10700-009-9049-2
[19] Osuna-Gómez, R., Hernández-Jiménez, B., Chalco-Cano, Y. and Ruiz-Garzón, G. (2017) New Efficiency Conditions for Multiobjective Interval-Valued Programming Problems. Information Sciences, 420, 235-248.
https://doi.org/10.1016/j.ins.2017.08.022
[20] Ahmad, I., Singh, D. and Dar, B.A. (2015) Optimality Conditions in Multiobjective Programming Problems with Interval Valued Objective Functions. Control and Cybernetics, 44, 19-45.
[21] Singh, D., Dar, B.A. and Kim, D.S. (2016) KKT Optimality Conditions in Interval Valued Multiobjective Programming with Generalized Differentiable Functions. European Journal of Operational Research, 254, 29-39.
https://doi.org/10.1016/j.ejor.2016.03.042