自由支配集下近似平衡约束向量优化问题的稳定性研究

曾悦; 彭再云; 梁仁莉; 邵重阳

doi:10.21656/1000-0887.410244

自由支配集下近似平衡约束向量优化问题的稳定性研究

doi: 10.21656/1000-0887.410244

重庆交通大学数学与统计学院，重庆 400074

基金项目:

国家自然科学基金（11301571）；重庆市基础与前沿研究项目（cstc2018jcyjAX0337）；重庆市巴渝学者计划；重庆市研究生导师团队建设项目（JDDSTD201802）；重庆市研究生教育创新基金（CYS20290）；重庆市高校创新研究群体项目（CXQT21021）

详细信息

作者简介:
曾悦（1997—），女，硕士生（E-mail: zengyueylmn@163.com）；彭再云（1980—），男，教授，博士，博士生导师(通讯作者. E-mail: pengzaiyun@126.com).

通讯作者:
彭再云（1980—），男，教授，博士，博士生导师(通讯作者. E-mail: pengzaiyun@126.com).

中图分类号: O175.29
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- 文章访问数: 905
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出版历程
- 收稿日期: 2020-12-17
- 修回日期: 2021-01-22
- 网络出版日期: 2021-09-29

Stability of Vector Optimization Problems Under Approximate Equilibrium Constraints via Free-Disposal Sets

College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, P.R.China

Funds:

The National Natural Science Foundation of China(11301571)

摘要

摘要: 在自由支配集下，对一类近似平衡约束向量优化问题（AOPVF）的稳定性进行研究.首先，在较弱的凸性假设下获得了约束集映射的Berge-半连续性和约束集的闭性、凸性和紧性结果.然后，在目标函数列Gamma-收敛的假设下，分别得到了AOPVF弱有效解映射Berge半连续和弱有效解集下Painlevé-Kuratowski收敛的充分条件，并给出例子说明结论是新颖和有意义的.
- 自由支配集 /
- Gamma-收敛 /
- Berge-半连续 /
- 下Painlevé-Kuratowski收敛
Abstract: The stability of vector optimization problems under approximate equilibrium constraints (AOPVF) via free-disposal sets was discussed. Firstly, the Berge-semicontinuity of the constraint set mapping and the closedness, the convexity and the compactness of the constraint set were obtained with the weaker convexity assumption. Moreover, under the assumption of Gamma-convergence for the objective functional sequences, the lower Painlevé-Kuratowski convergence of the weak efficient solution set and the Berge-semicontinuity of weak efficient solution mappings for AOPVF were obtained respectively. Some examples illustrate that the results are new and meaningful.
- free-disposal set /
- Gamma-convergence /
- Berge-semicontinuity /
- lower Painlevé-Kuratowski convergence

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参考文献(22)

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自由支配集下近似平衡约束向量优化问题的稳定性研究

doi: 10.21656/1000-0887.410244

作者简介:
曾悦（1997—），女，硕士生（E-mail: zengyueylmn@163.com）；彭再云（1980—），男，教授，博士，博士生导师(通讯作者. E-mail: pengzaiyun@126.com).

通讯作者:
彭再云（1980—），男，教授，博士，博士生导师(通讯作者. E-mail: pengzaiyun@126.com).

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Stability of Vector Optimization Problems Under Approximate Equilibrium Constraints via Free-Disposal Sets

计量

目录

留言板

自由支配集下近似平衡约束向量优化问题的稳定性研究

doi: 10.21656/1000-0887.410244

作者简介: 曾悦（1997—），女，硕士生（E-mail: zengyueylmn@163.com）；彭再云（1980—），男，教授，博士，博士生导师(通讯作者. E-mail: pengzaiyun@126.com).

通讯作者: 彭再云（1980—），男，教授，博士，博士生导师(通讯作者. E-mail: pengzaiyun@126.com).

计量

出版历程

Stability of Vector Optimization Problems Under Approximate Equilibrium Constraints via Free-Disposal Sets

计量

出版历程

目录

作者简介:
曾悦（1997—），女，硕士生（E-mail: zengyueylmn@163.com）；彭再云（1980—），男，教授，博士，博士生导师(通讯作者. E-mail: pengzaiyun@126.com).

通讯作者:
彭再云（1980—），男，教授，博士，博士生导师(通讯作者. E-mail: pengzaiyun@126.com).