Robust optimality and solution existence for multiobjective optimization problems under data uncertainty

In this paper, we examine robust optimality and solution existence for a multiobjective nonsmooth optimization problem involving data uncertainty. To this end, we first introduce the concept of an extended tangency variety associated with the feasible set and a tangency value set for the corresponding robust multiobjective optimization problem. We then show that the proposed tangency variety is unbounded whenever the feasible set of the considered problem is unbounded. We further establish that the robust multiobjective optimization problem can be equivalently reformulated as a relaxed optimization problem defined over the corresponding tangency variety. With the help of the problem reformulations and the tangency value set, we provide necessary/sufficient optimality conditions for weak Pareto solutions and investigate the existence of solutions to the underlying problem.