择一定理及向量优化问题的Benson真有效性

Alternative theorem and benson proper efficiency for vector optimization problems

在局部凸Hausdorff空间中,引入了近次似凸集值映射,建立了近次似凸集值映射下的择一定理.最后,获得了近次似凸集值映射向量优化问题标量下Benson真有效性的一个性质.

In this paper, nearly subconvexlike set-valued maps were introduced and the alternative theorem under its was obtained in locallyconvex Hausdorff spaces. Finally, a characterization of the benson proper efficiency for vector optimization problems of nearly subconvexlike set-valued maps was obtained in terms of scalarization.