集值优化问题全局极小解集的连通性

The connectedness of the globally minimal solution set for set-valued optimization problems

在Hausdorff局部凸空间中,讨论了集值优化问题全局极小解的连通性问题.证明了当目标函数为锥类凸集值映射时,其目标空间里的全局有效点集是连通的;若目标函数为弧式锥凸集值映射,则其全局极小解集也是连通的.

The eonnectedness of globally minimal solution set for set-valued optimization problems in Hausdorff locally convex space was discussed. The connectedness of the globally efficient point set was proved when objective functions were cone convexlike. When objective functions were arcwise cone convex set-valued mapping, then globally minimal solution set was also connected.