Second-order necessary optimality condition for weakly efficient solutions in constrained vector optimization problems

Abstract

In the paper, we study second-order necessary optimality conditions for a nonsmooth vector optimization problem with set, cone and equality constraints based on the concept of twice continuously directional derivatives in real Banach spaces. For the purpose above, we provide some concepts for weakly efficient solutions to such problem and present some characterizations on twice continuously directional differentiabilities for the class of real-valued functions. Under suitable assumptions, some primal and Fritz John-type dual second-order necessary optimality conditions for the locally weakly efficient solutions of such problem are provided as well. The second-order optimality conditions obtained are new or improve some recent existing ones in the literature.