This article deals with considering stability properties of Pareto minimal solutions to set optimization problems with the set less order relation in real topological Hausdorff vector spaces. We focus on studying the Painlevé–Kuratowski convergence of Pareto minimal elements in the image space. Employing convexity properties, we study the external stability of Pareto minimal solutions via weak ones. Then, we use converse properties to investigate external stability conditions to such problems where Pareto minimal solution sets and weak/ideal ones are distinct. For the internal stability, we propose a concept of compact convergence in the sense of Painlevé–Kuratowski and use it together with a domination property to analyze stability conditions for the reference problems.

本文讨论考虑Pareto极小解的稳定性，以在实际拓扑Hausdorff向量空间中用最小集序关系设置优化问题。我们专注于研究图像空间中帕累托极小元素的Painlevé-Kuratowski收敛性。利用凸性质，我们研究了通过弱解的帕累托极小解的外部稳定性。然后，我们使用相反的性质来研究外部稳定性条件，以解决其中Pareto最小解集与弱/理想解不同的这类问题。对于内部稳定性，我们提出了Painlevé-Kuratowski意义上的紧致收敛的概念，并将其与支配性一起用于分析参考问题的稳定性条件。