Abstract: 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.

Key words: Set-valued mapping, Henig efficiency, Subdifferential, stability