Extended B-Well-Posedness and Property (H) for Set-Valued Vector Optimization with Convexity

摘要

The purpose of this paper is to study the extended well-posedness in the sense of Bednarczuk for set-valued vector optimization. This notion of well-posedness can be interpreted as some sort of well-posedness under perturbation in terms of Hausdorff set-convergence. To investigate the extended B-well-posedness, we generalize property (H) due to Miglierina and Molho to the set-valued and perturbed case. Under a convexity assumption, we show that the extended B-well-posedness is closely related to property (H).