集值优化问题近似Henig真有效点的稳定性

Stability of Approximate Henig Proper Effective Point for Set-valued Optimization Problems

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。

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 Γ_(C) convergence of set-valued function sequence,compared the relationship between the Painlevé-Kuratowski convergence and Γ_(C) convergence,and found that the Painlevé-Kuratowski convergence is weaker than Γ_(C) 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.