一类集值优化最小解的存在性与适定性及应用

The Existence and Well-Posedness of Minimum Solutions for a Class of Set-Valued Optimization Problems with Applications

主要利用集值分析理论,探讨一类集值优化的最小解的存在性与l-Bz-适定性.首先给出了定义在向量空间中的集值映射的R+-局部包含性与R--弱转移下半连续性的概念,在此基础上,新定义了C(intC)-局部包含性与C^(Z)((intC)^(Z))-弱转移下半连续性,根据这些性质,给出了集值优化最小解的存在性与l-Bz-适定的充分条件.作为所获结果的应用,讨论了一类带不确定性的向量值博弈问题,给出了鲁棒纳什均衡的存在性与l-Bz-适定的充分条件.

This paper deals with the existence and l-Bz---well-posedness of the minimum solutions for a class of set-valued optimization problems by using the set valued analysis theory. First, in view of the introduced R+-local-inclusion property and R-weakly transfer lower semicontinuity in a vector space, a new definition of the C(intC)-local inclusion and lower semi-continuity with the C^(Z)((intC)^(Z))-weak transfer is given. Next, the sufficient conditions for the existence of minimum solutions for set-valued optimizations are presented by using the character mentioned above. Finally, as an application of the obtained results, a class of vector valued games with uncertainty is discussed and present sufficient conditions for the existence of a robust Nash equilibria with the l-Bz-well-posedness are presented.