Optimality conditions for a class of composite multiobjective nonsmooth optimization problems

In this paper, a class of composite multiobjective nonsmooth optimization problems with cone constraints is considered. Necessary optimality conditions for weak minimum are established in terms of Semi-infinite Gordan type theorem. η-generalized null space condition, which is a proper generalization of generalized null space condition, is proposed. Sufficient optimality conditions are obtained for weak minimum, Pareto minimum, Benson’s proper minimum under K-generalized invexity and η-generalized null space condition. Some examples are given to illustrate our main results.