This paper aims to study the well-posedness of semi-infinite set optimization problems. We first introduce a notion of global well-posedness for efficient solutions of the reference problems. This notion is then characterized in terms of qualitative properties of approximately minimal solution maps. Next, we extend this notion for perturbed problems obtained by perturbing both the objective set-valued maps and the constraints. Finally, we establish sufficient conditions for the proposed well-posedness by utilizing the Slater constraint qualification and converse properties of the objective set-valued maps.

中文翻译：

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半无限集优化问题的全局适定性

本文旨在研究半无限集优化问题的适定性。我们首先引入全局适定性的概念，以有效解决参考问题。然后用近似最小解图的定性属性来表征这个概念。接下来，我们将这个概念扩展到通过扰动目标集值映射和约束而获得的扰动问题。最后，我们利用 Slater 约束条件和目标集值映射的逆属性为所提出的适定性建立充分条件。