Semi-differentiability of the marginal mapping in vector optimization

We consider a parametric multiobjective optimization problem whose objective function and constraint set are not necessarily convex. We introduce the concept of uniform efficiency, characterize it and compare it with the well-known concepts of proper efficiency and normal efficiency. Then we establish the semi-differentiability of the marginal (efficient value) mapping and a formula to compute its semi-derivative at a uniformly efficient value. As an application we derive semi-differentiability of the marginal function for a problem in which the constraint set is given by a system of inequalities, and for a problem whose constraint set is a union of polyhedral convex sets. The results of this paper are not only new in the case of nonconvex multiobjective problems, but they also deepen some existing ones for the convex case.