In this paper, we study characterizations and necessary conditions for nondominated points of sets and nondominated solutions of vector-valued functions in vector optimization with variable domination structure. We study not only the case, where the intersection of all the involved domination sets has a nonzero element, but also the case, where it might be the singleton. While the first case has been studied earlier, the second case has not, to the best of our knowledge, done yet. Our results extend and improve the existing results in vector optimization with a fixed ordering cone and with a variable ordering structure.

中文翻译：

---

向量优化中非支配解的必要条件

在本文中，我们研究了具有可变支配结构的向量优化中向量值函数的非支配点和向量值函数的非支配解的特征和必要条件。我们不仅研究了所有涉及的支配集的交集都具有非零元素的情况，而且还研究了它可能是单例的情况。虽然早先已经研究了第一个案例，但据我们所知，第二个案例尚未完成。我们的结果扩展和改进了矢量优化中现有的结果，具有固定的排序锥和可变的排序结构。