Proper efficiency conditions and duality results for nonsmooth vector optimization in Banach spaces under (Φ,ρ)(Φ,ρ)-invexity

In this paper, a new class of nonsmooth nonconvex multiobjective programming problems in Banach spaces is considered. The sufficient optimality conditions for efficiency and proper efficiency are established under nonsmooth (Φ,ρ)(Φ,ρ)-invexity and generalized (Φ,ρ)(Φ,ρ)-invexity notions, after extending these concepts to the functions between Banach spaces. Further, Mond–Weir duality theorems are also established under (Φ,ρ)(Φ,ρ)-invexity for the considered vector optimization problems in Banach spaces.