向量优化中广义内部的一些注记

Remarks on Generalized Interior in Vector Optimization

在向量优化中,基于拓扑内部的集合的许多性质具有十分重要的作用,然而在无限维空间中存在许多拓扑内部为空的集合。因此,研究广义内部下集合的一些相应的性质特征则显得十分必要。首先归纳了向量优化中拓扑内部意义下集合的一些经典结果,进而通过一些具体的例子研究了这些经典结果在拟内部等广义内部意义下的情形。

Many characterizations via topological interior of sets have been playing an important role in vector optimization.However,there exist many sets with empty topological interior in infinite dimensional spaces.Hence,it is necessary to investigate the corresponding characterizations of sets in the sense of generalized interior.In this paper,we first summarize some classical results based on the topological interior in vector optimization.Furthermore,we investigate some corresponding cases in the sense of generalized interior such as quasi interior by means of some concrete examples.