Painlevé-Kuratowski Stability of the Solution Sets to Perturbed Vector Generalized Systems

In this paper, stability results of solution mappings to perturbed vector generalized system are studied. Firstly, without the assumption of monotonicity, the Painlevé-Kuratowski convergence of global efficient solution sets of a family of perturbed problems to the corresponding global efficient solution set of the generalized system is obtained, where the perturbations are performed on both the objective function and the feasible set. Then, the density and Painlevé-Kuratowski convergence results of efficient solution sets are established by using gamma convergence, which is weaker than the assumption of continuous convergence. These results extend and improve the recent ones in the literature.