Lower and upper Ginchev derivatives of vector functions and their applications to multiobjective optimization

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.