集值优化问题近似Henig真有效点的稳定性
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Stability of Approximate Henig Proper Effective Point
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    集值优化问题是十分贴近实际生活的一类数学模型,具有广泛的应用前景.〖BP)〗 针对集值优化问题近似Henig真有效点,提出在目标集值优化问题的映射及可行域均扰动的情形下,建立C凸集值优化问题近似Henig真有效点的稳定性结果,将近似Henig真有效点的稳定性研究从向量值优化问题推广到集值优化问题中。首先给出集值映射序列ΓC收敛的概念,比较了集值映射序列PainlevéKuratowski收敛与ΓC收敛性之间收敛强弱的关系,发现PainlevéKuratowski收敛弱于ΓC收敛;其次将PainlevéKuratowski收敛应用于建立近似Henig真有效点的稳定性结果中,在扰动集值优化问题的问题数据PainlevéKuratowski收敛到目标集值优化问题的问题数据情况下,获得了集值优化问题近似Henig真有效点的抗干扰稳定性结果,该结果对数值计算分析中集值优化问题近似Henig真有效点的稳定性研究有着重要的理论分析价值。

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    The setvalued optimization problem,with a wide application prospects,is a kind of mathematical model which is very close to our practical life. 〖BP)〗Aiming at the setvalued optimization problem of approximate Henig proper effective point, we proposed to establish the stability results of the approximate Henig proper effective point for the C-convex setvalued optimization problem under the condition that the functions and feasible region of the objective setvalued optimization problems are perturbed. And the stability study of approximate Henig proper efficient points is extended from vectorvalued optimization problems to set valued optimization problems. Firstly, we gave the concept of ΓC convergence of setvalued function sequence, compared the relationship between the PainlevéKuratowski convergence and ΓC convergence, and found that the PainlevéKuratowski convergence is weaker than ΓC convergence. Secondly, we used the PainleveKuratowski convergence to establish the stability result of approximate Henig proper efficient points. We obtain the antiinterference stability results of the approximate Henig proper effective points for the setvalued optimization problem when the data of the disturbed setvalued optimization problem PainleveKuratowski converges to the data of the objective setvalued optimization problem. The results have an important theoretical value for the stability study of approximate Henig proper effective points of setvalued optimization problems in numerical calculation and analysis.

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胡瑞婷.集值优化问题近似Henig真有效点的稳定性[J].重庆工商大学学报(自然科学版),2022,39(2):53-58
HU Rui-ting. Stability of Approximate Henig Proper Effective Point[J]. Journal of Chongqing Technology and Business University(Natural Science Edition),2022,39(2):53-58

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  • 在线发布日期: 2022-03-25
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