On Hadamard well-posedness of families of Pareto optimization problems

This paper deals with the well-posedness of families of finite dimensional vector optimization problems ordered by components (Pareto problem). For this problem, two Hadamard well-posedness concepts are introduced. These concepts involve the existence and uniqueness of efficient/weak efficient solutions, and also the continuous behavior of these solutions with respect to perturbations of the data. The perturbations in the last property are formulated through a variational convergence notion of the objective functions and by considering approximate solutions of the perturbed problems. Necessary and sufficient conditions for the well-posedness of Pareto optimization problems are obtained in general, and also under convexity and quasiconvexity assumptions. To do this, asymptotic mathematical tools are employed. Finally, it is proved that the convex Pareto optimization problems are “essentially” well-posed in the sense of category theory.