摘要
本简报指出:若是部凸空间中存在一个凸锥它既具紧基,又具非空内部,则该局部凸空间必为有限维的.利用局部凸空间的对偶理论,在不对序锥附近加其他条件的前提下,我们获得了Benson真有效点的对偶特征.由此,我们给出了几乎锥次凸状集值映照的向量优化问题的Benson真极小元的标量化定理.
In this brief report, it is pointed out that if a locally convex space has a convex cone with a compact base and with a nonempty interior, then it is finite dimensional. By using the dual theory of locally convex spaces, we obtain a dual characterization for Benson proper efficient points without any additional assumption on the ordering cone. From this we give a scalarization theorem for Benson proper minimizers of vector optimization problems with nearly cone-subconvexlike set-valued maps.
出处
《苏州大学学报（自然科学版）》
CAS
2006年第3期93-94,共2页
Journal of Soochow University(Natural Science Edition)
基金
国家自然科学基金资助项目(10571035)
关键词
局部凸空间
对偶
真有效性
标量化
几乎锥次凸状集值映照
locally convex space
dual
Benson proper efficiency
scalarization
nearly cone-subconvexlike setvalued map
