Optimality and stability conditions for Benson efficient solutions in vector optimization problems

In this paper, we explore two fundamental properties of Benson efficient solutions for vector optimization problems with set-valued objective mappings based on the recession cone of a nonempty set.Specifically, we focus on the optimality conditions and stability properties of these solutions.First, we employ the scalarization method to establish sufficient and necessary optimality conditions for the unconstrained optimization problems.Then, by utilizing these techniques along with a generalized Slater constraint qualification, we obtain the corresponding results for reference problems with constraints.When the data of the considered problems is perturbed by parameters given in parameter spaces, we use scalar representations of the solutions in combination with generalized convexity concepts to study the stability of Benson efficient solution mappings in the sense of semicontinuity for these parametric optimization problems.Various examples are given to highlight the applications and distinctions of the results achieved in this study.