Scalarization and optimality conditions for strict minimizers in multiobjective optimization via contingent epiderivatives

In this paper necessary and sufficient conditions for strict minimizers of a general vector optimization problem are given by means of different notions of graphical or epigraphical derivatives, extending some existing results in the literature. In first place, these conditions are established by means of contingent derivatives and secondly, by applying a nonconvex separation result, in terms of contingent epiderivatives and hypoderivatives. Moreover, through a variational approach, a scalarization method is developed in order to obtain scalar versions of these results.