Lower and upper Ginchev derivatives of vector functions and their applications to multiobjective optimization
El-Desouky Rahmo, Aleksandra Stasiak, Marcin Studniarski · Optimization Letters · 2013
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.