Higher-order conditions for strict local Pareto minima in terms of generalized lower and upper directional derivatives

We introduce lower and upper limits of vector-valued functions with respect to the usual positive cone in a finite-dimensional space. Using these concepts, we extend the definitions of mm-th order lower and upper directional derivatives introduced in Studniarski (1986) [1] to vector-valued functions, and prove some necessary and sufficient conditions for strict local Pareto minimizers of order mm.