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引用本文:	胡瑞婷.集值优化问题近似Henig真有效点的稳定性(J/M/D/N,J:杂志，M：书，D：论文，N：报纸).期刊名称,2022，39（2）：53-58
	CHEN X. Adap tive slidingmode contr ol for discrete2ti me multi2inputmulti2 out put systems[ J ]. Aut omatica, 2006, 42(6): 4272-435

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集值优化问题近似Henig真有效点的稳定性
胡瑞婷
重庆工商大学数学与统计学院，重庆 400067

摘要:

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。

关键词: C凸近似Henig真有效点 Painlevé Kuratowski收敛稳定性

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Stability of Approximate Henig Proper Effective Point

HU Rui-ting

School of Mathematics and Statistics， Chongqing Technology and Business University， Chongqing 400067， China

Abstract:

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.

Key words: C-convex approximate Henig proper efficient point Painlevé kuratowski convergence stability