Nondifferentiable (Phi, rho)-type I and generalized (Phi, rho)-type I functions in nonsmooth vector optimization

In this paper, new classes of nondifferentiable generalized invex functions arc introduced. Further, nonsmooth vector optimization problems with functions belonging to the introduced classes of (generalized) (Phi, rho)-type I functions are considered. Sufficient optimality conditions and duality results for such classes of nonsmooth vector optimization problems are established. It turns out that the presented results are proved also for such nonconvex vector optimization problems in which not all functions constituting them possess the fundamental property of invexity.