多目标主从向量集值优化Benson真有效解的连通性

Connectedness of Benson proper efficiency in vector top base optimization of set valued maps

讨论了向量集值优化问题Benson真有效集及Benson真有效解的连通性 ,证明了当目标函数为某类锥凸集值映射 ,序锥具有紧基时非空紧凸集上的Benson真有效点及Benson真有效解均为连通的 .

Connectedness of Benson proper efficient set and Benson proper efficient solution set of vector optimization of set valued maps are investigated. The results obtained actually imply that the Benson proper efficient set of the objective space is connected when the objective function is cone subconvexlike, and that if the objective function is a cone convex set valued mapping, the Benson proper efficient solution set is connected too. As an interesting application of the results, the connectednesses of the Benson proper efficient set and the Benson proper efficient solution set for the vector top base optimization of set valued maps are obtained.