孟旭东. 含参集值优化问题近似解集的稳定性[J]. 云南大学学报(自然科学版), 2022, 44(4): 663-674. doi: 10.7540/j.ynu.20210329
引用本文: 孟旭东. 含参集值优化问题近似解集的稳定性[J]. 云南大学学报(自然科学版), 2022, 44(4): 663-674. doi: 10.7540/j.ynu.20210329
MENG Xu-dong. Stability of approximate solutions set for parametric set-valued optimization problem[J]. Journal of Yunnan University: Natural Sciences Edition, 2022, 44(4): 663-674. DOI: 10.7540/j.ynu.20210329
Citation: MENG Xu-dong. Stability of approximate solutions set for parametric set-valued optimization problem[J]. Journal of Yunnan University: Natural Sciences Edition, 2022, 44(4): 663-674. DOI: 10.7540/j.ynu.20210329

含参集值优化问题近似解集的稳定性

Stability of approximate solutions set for parametric set-valued optimization problem

  • 摘要:
    在赋范线性空间中讨论了含参集值优化问题近似解集的稳定性. 首先,给出了含参集值优化问题2类(弱)近似解的概念及其性质关系. 其次,在目标函数集值映射具严格近似上(下)锥凸性假设下,获得了含参集值优化问题2类(弱)近似解集的上半连续性定理. 最后,结合水平映射的方法研究了含参集值优化问题2类(弱)近似解集的下半连续最优性充分条件.

     

    Abstract: The stability of approximate solutions set to parametric set-valued optimization problem is discussed in normed linear space. Firstly, the concepts and properties for two kinds of (weak) approximate solutions to parametric set-valued optimization problem are given. Secondly, under the assumption that the set-valued mapping of objective function having strict approximate upper (lower) cone convexity, the upper semicontinuity theorems for two kinds of (weak) approximate solutions set to parametric set-valued optimization problems are obtained. Finally, the sufficient conditions for the lower semicontinuity of two kinds of (weak) approximate solution sets to parametric set-valued optimization problems are studied by using the method of level mapping.

     

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