集值映射的超有效广义梯度

The Super Efficient Generalized Gradient of Set-valued Map

在Hausdorff局部凸拓扑线性空间中,对于集值优化问题(SOP),利用contingent上图切导数,引进了集值映射超有效意义下的广义梯度,在目标函数为锥类凸的集值映射并且具有连通性条件下,利用凸集分离定理和contingent上图切导数,证明了集值映射超有效广义梯度的存在性,得到了集值映射超有效广义梯度的等价刻画等定理。

In Hausdorff locally convex spaces, for the set-valued vector optimization problem （SOP）, the super efficient generalized gradient of set-valued map is introduced by measns of contingent epiderivative. Under the condition of connectedness and D-convexlikeness, its existence is proved and the equivalent characterization for this super efficient generalized gradient is established by the separation theorem of convex sets and contingent epiderivarive.