Generalized Gradients in Sense of Henig Efficiency for Set-Valued Maps

In this paper, we deal with the Henig efficiency for set-valued optimization problems in sense of subdifferential. By the epiderivative for a set-valued mapping, the concepts of the generalized gradient and subdifferential for efficiency are introduced. Based upon the separation theorem, the existence for Henig subdifferential is established, and the optimality condition for Henig efficient solutions of vector set-valued optimization is obtained by the subdifferential in terms of Henig efficiency. The results deepen and enrich the content of optimization theory and applications.