Optimality and duality in nonsmooth composite vector optimization and applications

This article is devoted to the study of a nonsmooth composite vector optimization problem (P for brevity). We apply some advanced tools of variational analysis and generalized differentiation to establish necessary conditions for (weakly) efficient solutions of (P). Sufficient conditions for the existence of such solutions to (P) are also provided by means of proposing the use of (strictly) generalized convex composite vector functions with respect to a cone. We also state a dual problem to (P) and explore weak, strong and converse duality relations. In addition, applications to a multiobjective approximation problem and a composite multiobjective problem with linear operators are deployed.