Abstract: Firstly, some necessarily basic concepts and an important lemma were given. Secondly, some important properties of generalized higher-order tangent sets were discussed. Finally, by virtue of those properties and the Gerstewitz's nonconvex separation functional, necessary and sufficient optimality conditions were obtained for weakly Benson proper efficient solutions of set-valued optimization problems without any convexity assumption on objective
and constraint mappings. Moreover, two examples were given to show that the result obtained is a generalization to the corresponding results in literatures.

Key words: generalized higher order contingent sets, nonconvex separation functional, Benson proper efficient solutions, higher-order optimality conditions, set-valued optimization, generalized higher order contingent sets, nonconvex separation functional, Benson proper efficient solutions, higher-order optimality conditions