集值映射的ε-强次微分及应用

 在Hausdorff局部凸拓扑向量空间中引进了集值映射ε-强有效次微分的概念。在一定条件下, 通过凸集分离定理证明了该次微分的存在性定理。 作为应用,得到了约束集值优化问题ε-强有效解在Lagrange乘子形式下的最优性必要条件。

ε-strongly subdifferential of set-valued mapping and application

In Hausdorff locally convex topological vector spaces, the concept of ε-strongly efficient subdifferential for a set-valued mapping was introduced. Under certain condition, by using the convex set separation theorem, the existence theorem for ε-strongly efficient subdifferential was proposed. As an application, the necessary optimality condition of the constraint set-valued optimization problem for ε-strongly efficient solutions was established in terms of Lagrange multiplier by using the concept of ε strongly efficient subdifferential for set valued mapping.