Optimality conditions for a nonconvex set-valued optimization problem

In this paper we study necessary and sufficient optimality conditions for a set-valued optimization problem. Convexity of the multifunction and the domain is not required. A definition of KK-approximating multifunction is introduced. This multifunction is the differentiability notion applied to the problem. A characterization of weak minimizers is obtained for invex and generalized KK-convexlike multifunctions using the Lagrange multiplier rule.