Second-Order Necessary and Sufficient Optimality Conditions for Constrained Vector Equilibrium Problem with Applications

In this paper, we study a generalized convex vector equilibrium problem with cone and set constraints in real Banach spaces. We provide some basic characterizations on generalized convexity for the first- and second-order directional derivatives. We obtain Kuhn–Tucker second-order necessary and sufficient optimality conditions for efficiency to such problem under suitable assumptions on the generalized convexity of objective and constraint functions. As an application, we present Kuhn–Tucker second-order necessary and sufficient optimality conditions to a generalized convex vector variational inequality problem and a generalized convex vector optimization problem with constraints. Some examples are also given to demonstrate the main results of the paper.