The Henig Efficient Subdifferential of Set-valued Mapping and Stability
集值映射的Henig有效次微分及其稳定性

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 existence 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.