向量优化中改进集的一些注记

Some Remarks on Improvement Sets in Vector Optimization

首先利用凸集分离定理和回收锥等工具给出了改进集的几个一般性质,进一步提出了基于改进集定义的E-有效解集的两个新性质,最后通过例子指出Chicco等人证明的关于E-有效解集的一个性质是不正确的.

In this paper ,we first give several general properties about improvement set ,using some tools like the separation theorem for convex sets and recession cone .Furthermore ,we propose two new characterizations of the set of E-efficient solution defined by improvement set .Finally ,using some examples ,we point out that a characterization proposed by Chicco et al about the set of E-efficient solution is not valid .