Qualitative Properties of Robust Benson Efficient Solutions of Uncertain Vector Optimization Problems

In this paper, we consider both unconstrained and constrained uncertain vector optimization problems involving free disposal sets, and study the qualitative properties of their robust Benson efficient solutions. First, we discuss necessary and sufficient optimality conditions for the robust Benson efficient solutions of these problems using the linear scalarization method. Then, by utilizing this approach, we investigate the semicontinuity properties of the solution maps when the problem data is perturbed by parameters given in parameter spaces. Finally, we suggest concepts of approximate robust Benson efficient solutions and investigate Hausdorff well-posedness conditions for such problems with respect to these approximate solutions. Several examples are provided to illustrate the applicability and novelty of the results obtained in this study.