Ekeland变分原理导出的向量均衡系统解的存在性

Existence for System of Vector Equilibriums via Ekeland’s Principle

本文研究了定义在度量空间上的向量均衡系统解的存在性问题。利用非线性标量化方法,将向量优化问题转化为数量优化问题,得到了Ekeland变分原理的一个向量形式推广。用向量形式Ekeland变分原理,证明了向量均衡系统解的存在性定理。结果表明,如果函数满足向量形式Ekeland变分原理和上半连续性条件,那么向量均衡系统的解集非空。

This paper studies the existence of solutions for the system of vector equilibrium problem on metric spaces. By using the nonlinear scalarilization method, vector optimization problems are transformed into scalar optimization problems. Sequentially, the Ekeland’s variational principle is generalized to the vector form Ekeland’s variational principle.Using the vector form Ekeland’s variational principle, we establish an existence theorem for the system of vector equilibrium problem. Our results show that, if the function satisfies the vector form Ekeland’s variational and the upper semi-continuity assumption, then the set of solutions for the system of vector equilibrium problem is nonempty.