集值映射的Henig有效次微分及其稳定性

The Henig Efficient Subdifferential of Set-valued Mapping and Stability

该文在赋范线性空间中对集值映射引入锥-Henig有效次梯度和锥-Henig有效次微分的概念.借助凸集分离定理证明了锥-Henig有效次微分的存在性,并且建立了线性泛函为锥-Henig有效次梯度的充要条件。最后,对于一类参数扰动集值优化问题讨论了其在Henig有效意义下的稳定性.

In normed linear spaces, the concepts of cone-Henig efficient subgradient and cone- Henig efficient subdifferential for a set-valued mapping are introduced. By using the convex set separation theorem, the exis.tence theorem for cone-Henig efficient subdifferential is proposed, and the sufficient and necessary condition for a linear functional being a cone-Henig efficient subgradient is established. Finally, the stability problem for a kind of perturbed set-valued opimization problem is considered in sense of Henig efficiency.