Image space analysis and separation for G-semidifferentiable vector problems

This paper aims at studying, in the image space, an approximation of a vector optimization problem obtained by substituting the involved functions with their $G$-derivatives. It is shown that, under the hypothesis of $G$-differentiability, the existence of a semistationary point is equivalent to the linear separation between the image of the approximated problem and a suitable convex subset of the image space. Applications to optimality conditions are provided.