| 自由支配集下近似平衡约束向量优化问题的稳定性研究 |
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| 引用本文： | 曾悦,彭再云,梁仁莉,邵重阳. 自由支配集下近似平衡约束向量优化问题的稳定性研究[J]. 应用数学和力学, 2021, 42(9): 958-967. DOI: 10.21656/1000-0887.410244 |
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| 作者姓名： | 曾悦 彭再云 梁仁莉 邵重阳 |
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| 作者单位： | 重庆交通大学 数学与统计学院， 重庆 400074 |
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| 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） |
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| 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.
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| 关 键 词： | 自由支配集 Gamma-收敛 Berge-半连续 下Painlevé-Kuratowski收敛 |
| 收稿时间： | 2020-12-17 |
Stability of Vector Optimization Problems Under Approximate Equilibrium Constraints via Free-Disposal Sets |
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| Affiliation: | College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, P.R.China |
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| 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. |
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