Abstract
Based on the definitions of lower and upper limits of vector functions introduced in Rahmo and Studniarski (J Math Anal Appl 393:212-221, 2012), we extend the lower and upper Ginchev directional derivatives to functions with values in finite-dimensional spaces where partial order is introduced by a polyhedral cone. This allows us to obtain some modifications of the optimality conditions from Luu (Higher-order optimality conditions in nonsmooth cone-constrained multiobjective programming. Institute of Mathematics, Hanoi, Vietnam 2008) with weakened assumptions on the minimized function.