This article investigates stability conditions for set optimization problems with the set less order relation in the senses of Panilevé–Kuratowski and Hausdorff convergence. Properties of various kinds of convergences for elements in the image space are discussed. Taking such properties into account, formulations of internal and external stability of the solutions are studied in the image space in terms of the convergence of a solution sets sequence of perturbed set optimization problems to a solution set of the given problem.

中文翻译：

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具有集合少阶关系的集合优化问题解的收敛性

本文研究了在 Panilevé-Kuratowski 和 Hausdorff 收敛意义上的具有集合少阶关系的集合优化问题的稳定性条件。讨论了图像空间中元素的各种收敛的性质。考虑到这些特性，根据扰动集优化问题的解集序列到给定问题的解集的收敛性，研究了图像空间中解的内部和外部稳定性的公式。