This article aims to elaborate on various notions of Levitin–Polyak well-posedness for set optimization problems concerning Pareto efficient solutions. These notions are categorized into two classes including pointwise and global Levitin–Polyak well-posedness. We give various characterizations of both pointwise and global Levitin–Polyak well-posedness notions for set optimization problems. The hierarchical structure of their relationships is also established. Under suitable conditions on the input data of set optimization problems, we investigate the closedness of Pareto efficient solution sets in which they are different from the weakly efficient ones. Furthermore, we provide sufficient conditions for global Levitin–Polyak well-posedness properties of the reference problems without imposing the information on efficient solution sets.

本文旨在详细阐述有关帕累托有效解的集合优化问题的 Levitin-Polyak 适定性的各种概念。这些概念分为两​​类，包括逐点和全局 Levitin-Polyak 适定性。我们给出了集合优化问题的逐点和全局 Levitin-Polyak 适定概念的各种特征。也建立了他们关系的层次结构。在集合优化问题的输入数据的合适条件下，我们研究了帕累托有效解集与弱有效解集不同的封闭性。此外，我们为参考问题的全局 Levitin-Polyak 适定性质提供了充分条件，而无需将信息强加于有效解决方案集。