Vector Optimization Involving Preinvex Functions in Banach Spaces

In this paper, we deal with a vector optimization problem where all functions involved are preinvex functions between Banach spaces. Based upon the properties of a Lagrangian mapping and convex cones, the saddle point conditions and duality theorems are proposed. Finally, the relationship between a vector variational inequality and an unconstraint vector optimization problem is discussed. The results deepen and enrich the content of optimization theory and applications.