Positivity ( IF 1 ) Pub Date : 2020-05-21 , DOI: 10.1007/s11117-020-00766-6 Chuang-liang Zhang , Nan-jing Huang
In this paper, some properties of the lower (upper) semi-continuity for set-valued maps taking values in an abstract pre-ordered set are showed, which are then applied to study the existence of solutions for abstract set optimization problems. Moreover, some relationships between minimal solutions for abstract set-valued optimization problems with the vector and set criteria are given under mild conditions. As applications, existence results of solutions for set optimization problems are applied to obtain the existence of saddle points for the set-valued map taking values in the pre-ordered set with the set criterion and of solutions for vector optimization problems whose image space is a real vector space not necessarily endowed with a topology.
中文翻译:
广义半连续集值映射的集优化问题及其应用
在本文中,显示了在抽象预排序集中获取值的集值映射的下(上)半连续性的一些属性,然后将其用于研究抽象集优化问题的解的存在性。此外,在温和条件下,给出了带有向量的抽象集值优化问题的最小解与集准则之间的一些关系。作为应用,将集优化问题的解的存在结果应用于获得具有设置准则的预排序集中值的集值映射的鞍点的存在以及图像空间为a的向量优化问题的解的存在。实矢量空间不一定具有拓扑。