Optimality conditions for a nonconvex set-valued optimization problem

Abstract: 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 -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 -convexlike multifunctions using the Lagrange multiplier rule. [Copyright &y& Elsevier]