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非凸多目标优化模型的一类鲁棒逼近最优性条件

赵丹 孙祥凯

赵丹, 孙祥凯. 非凸多目标优化模型的一类鲁棒逼近最优性条件[J]. 应用数学和力学, 2019, 40(6): 694-700. doi: 10.21656/1000-0887.390289
引用本文: 赵丹, 孙祥凯. 非凸多目标优化模型的一类鲁棒逼近最优性条件[J]. 应用数学和力学, 2019, 40(6): 694-700. doi: 10.21656/1000-0887.390289
ZHAO Dan, SUN Xiangkai. Some Robust Approximate Optimality Conditions for Nonconvex Multi-Objective Optimization Problems[J]. Applied Mathematics and Mechanics, 2019, 40(6): 694-700. doi: 10.21656/1000-0887.390289
Citation: ZHAO Dan, SUN Xiangkai. Some Robust Approximate Optimality Conditions for Nonconvex Multi-Objective Optimization Problems[J]. Applied Mathematics and Mechanics, 2019, 40(6): 694-700. doi: 10.21656/1000-0887.390289

非凸多目标优化模型的一类鲁棒逼近最优性条件

doi: 10.21656/1000-0887.390289
基金项目: 国家自然科学基金(11701057);重庆市自然科学基金重点项目(cstc2017jcyjBX0032);河南省教育厅人文社科项目(2019-ZZJH-202)
详细信息
    作者简介:

    赵丹(1982—),女,讲师,硕士(E-mail: zd_1008@126.com);孙祥凯(1984—),男,教授,博士(通讯作者. E-mail: sxkcqu@163.com).

  • 中图分类号: O221.6;O224

Some Robust Approximate Optimality Conditions for Nonconvex Multi-Objective Optimization Problems

Funds: The National Natural Science Foundation of China(11701057)
  • 摘要: 通过引入一类非凸多目标不确定优化问题,借助鲁棒优化方法,先建立了该不确定多目标优化问题的鲁棒对应模型;再借助标量化方法和广义次微分性质,刻画了该不确定多目标优化问题的鲁棒拟逼近有效解的最优性条件,推广和改进了相关文献的结论.
  • [1] LUC D T. Theory of Vector Optimization [M]. Berlin: Springer-Verlag, 1989.
    [2] BOT R I, GRAD S M, WANKA G. Duality in Vector Optimization [M]. Berlin: Springer-Verlag, 2009.
    [3] 彭再云, 李科科, 张石生. D-η-E- 半预不变凸映射与向量优化[J]. 应用数学和力学, 2014,35(9): 1020-1032.(PENG Zaiyun, LI Keke, ZHANG Shisheng. D-η-E -semipreinvex vector mappings and vector optimization[J]. Applied Mathematics and Mechanics,2014,35(9): 1020-1032.(in Chinese))
    [4] 赵勇, 彭再云, 张石生. 向量优化问题有效点集的稳定性[J]. 应用数学和力学, 2013,34(6): 643-650.(ZHAO Yong, PENG Zaiyun, ZHANG Shisheng. Stability of the sets of effective points of vector valued optimization problems[J]. Applied Mathematics and Mechanics,2013,〖STHZ〗 34(6): 643-650.(in Chinese))
    [5] 陈望, 周志昂. 基于改进集的带约束集值向量均衡问题的最优性条件[J]. 应用数学和力学, 2018,39(10): 1189-1197.(CHEN Wang, ZHOU Zhiang. Optimality conditions for set-valued vector equilibrium problems with constraints involving improvement sets[J]. Applied Mathematics and Mechanics,2018,39(10): 1189-1197.(in Chinese))
    [6] BEN-TAL A, GHAOUI L E, NEMIROVSKI A. Robust Optimization [M]. Princeton: Princeton University Press, 2009.
    [7] LEE G M, LEE J H. On nonsmooth optimality theorems for robust multiobjective optimization problems[J]. Journal of Nonlinear and Convex Analysis,2015,16(10): 2039-2052.
    [8] EHRGOTT M, IDE J, SCHBEL A. Minmax robustness for multi-objective optimization problems[J]. European Journal of Operational Research,2014,239(1): 17-31.
    [9] SUN X K, PENG Z Y, GUO X L. Some characterizations of robust optimal solutions for uncertain convex optimization problems[J]. Optimization Letters,2016,10(7): 1463-1478.
    [10] FAKHAR M, MAHYARINIA M R, ZAFARANI J. On nonsmooth robust multiobjective optimization under generalized convexity with applications to portfolio optimization[J]. European Journal of Operational Research,2018,265(1): 39-48.
    [11] LORIDAN P. ε-solutions in vector minimization problems[J]. Journal of Optimization Theory and Application,1984,43(2): 265-276.
    [12] SON T Q, STRODIOT J J, NGUYEN V H. ε-optimality and ε-Lagrangian duality for a nonconvex programming problem with an infinite number of constraints[J]. Journal of Optimization Theory and Application,2009,141(2): 389-409.
    [13] SON T Q, KIM D S. ε-mixed type duality for nonconvex multiobjective programs with an infinite number of constraints[J]. Journal of Global Optimization,2013,57(2): 447-465.
    [14] SUN X K, LI X B, LONG X J, et al. On robust approximate optimal solutions for uncertain convex optimization and applications to multi-objective optimization[J]. Pacific Journal of Optimization,2017,13(4): 621-643.
    [15] CLARKE F H. Optimization and Nonsmooth Analysis [M]. New York: John Wiley & Sons, 1983.
    [16] MIFFLIN R. Semismooth and semiconvex functions in constrained optimization[J]. SIAM Journal on Control and Optimization,1977,15(6): 959-972.
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出版历程
  • 收稿日期:  2018-11-16
  • 修回日期:  2019-04-10
  • 刊出日期:  2019-06-01

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