Set-valued optimization which is an extension of vector optimization to
set-valued problems is a growing branch of applied mathematics. The
application of vector optimization technics to set-valued problems and the
investigation of optimality conditions has been of enormous interest in the
research of optimization problems. In this paper we have considered a Mayer
type problem governed by a discrete inclusion system with Lipschitzian
set-valued mappings. A necessary condition for K-optimal solutions of the
problem is given via local approximations which is considered the lower and
upper tangent cones of a set and the lower derivative of the set-valued
mappings.