| 向量优化问题有效点集的稳定性 |
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| 引用本文： | 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. |
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| 作者姓名： | 赵勇 彭再云 张石生 |
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| 作者单位： | 1重庆师范大学 数学学院, 重庆 400047;2重庆交通大学 理学院, 重庆 400074;3云南财经大学 数学与统计学院, 昆明 650224 |
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| 基金项目： | 国家自然科学基金资助项目，重庆市自然科学基金资助项目，重庆市教委资助项目 |
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| 摘 要： | 在不需要紧性假设下,利用拟C-凸函数及回收锥的性质，建立了向量优化问题有效点集的稳定性, 获得了一列目标函数和可行集均扰动情形下的向量优化问题与对应的向量优化问题有效点集的Painlevé Kuratowski内收敛性结果．所得结果推广和改进了相关文献(Attouch H, Riahi H. Stability results for Ekeland’s ε-variational principle and cone extremal solution; Huang X X. Stability in vector-valued and set-valued optimization)中的相应结果, 并给出例子说明了所得结果的正确性.
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| 关 键 词： | 向量优化问题 Painlevé-Kuratowski收敛性 稳定性 |
| 收稿时间： | 2013-04-27 |
Stability of the Sets of Efficient Points of Vector-Valued Optimization Problems |
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| Institution: | 1Department of Mathematics, Chongqing Normal University,Chongqing 400047, P.R.China;2Department of Mathematics, Chongqing Jiaotong University, Chongqing 400074, P.R.China;3Department of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunmin 650224, P.R.China |
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| Abstract: | By using quasi C-convex function and recession cone property, the stability of efficient points sets to vector optimization problems without the assumption of compactness was established.The lower part of the Painlevé-Kuratowski convergence of the sets for efficient points of perturbed problems to the corresponding efficient sets for the vector optimization problems was obtained, where the perturbation was performed on both the objective function and the feasible set. These results extend and improve the corresponding ones in the literature (Attouch H, Riahi H. Stability results for Ekeland’s ε-variational principle and cone extremal solution; Huang X X. Stability in vector-valued and set-valued optimization), then examples are given to illustrate our main results. |
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| Keywords: | vector optimization problem Painlevé-Kuratowski convergence stability |
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