In this paper, we give some properties concerned with weak minimal solutions of nonconvex set optimization problems. We also give some properties of the nonconvex separation functional and apply them to characterize weak minimal solutions of nonconvex set optimization problems. Moreover, we derive some new existence results for weak minimal solutions of nonconvex set optimization problems whose image spaces have no topology. Finally, we establish a set-valued version of Ekeland’s variational principle via set relations and present a weak minimization for a nonconvex set optimization problem. As applications, we obtain the existence of weak minimal solutions for nonconvex vector optimization problems.

在本文中，我们给出了一些与非凸集优化问题的弱极小解有关的性质。我们还给出了非凸分离泛函的一些性质，并将它们应用于表征非凸集优化问题的弱极小解。此外，对于图像空间没有拓扑结构的非凸集优化问题的弱极小解，我们推导出了一些新的存在结果。最后，我们通过集合关系建立 Ekeland 变分原理的集合值版本，并为非凸集优化问题提供弱最小化。作为应用，我们获得了非凸向量优化问题的弱极小解的存在性。