The emphasis of the paper is to examine the essential stability of efficient solutions for semicontinuous vector optimization problems, subject to the perturbation of objective function and feasible set. We obtain sufficient conditions for existence and characterization of essential efficient solutions, essential sets and essential components, where the efficient solutions are governed by an arbitrary preference relation in a real normed linear space. Further, we establish the density of the set of stable vector optimization problems in the sense of Baire category. We also exhibit that essential stability is weaker than examining continuity aspects of solution sets.

中文翻译：

---

统一向量优化中的基本稳定性

本文的重点是研究受目标函数和可行集干扰的半连续向量优化问题有效解的本质稳定性。我们为基本有效解，基本集和基本组件的存在和特征提供了充分的条件，其中有效解由实范数线性空间中的任意偏好关系支配。此外，我们从Baire类别的角度确定了一组稳定的矢量优化问题的密度。我们还展示出，本质稳定性比检查解决方案集的连续性方面要弱。