数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (5): 1670-1676.doi: 10.1016/S0252-9602(14)60113-2

• 论文 • 上一篇    

NON-CONFLICTING ORDERING CONES AND VECTOR OPTIMIZATION IN INDUCTIVE LIMITS

丘京辉   

  1. School of Mathematical Sciences, Soochow University, Suzhou 215006, China
  • 收稿日期:2012-06-14 修回日期:2014-06-09 出版日期:2014-09-20 发布日期:2014-09-20
  • 基金资助:

    This research was supported by the National Natural Science Foundation of China (10871141).

NON-CONFLICTING ORDERING CONES AND VECTOR OPTIMIZATION IN INDUCTIVE LIMITS

 QIU Jing-Hui   

  1. School of Mathematical Sciences, Soochow University, Suzhou 215006, China
  • Received:2012-06-14 Revised:2014-06-09 Online:2014-09-20 Published:2014-09-20
  • Supported by:

    This research was supported by the National Natural Science Foundation of China (10871141).

摘要:

Let (Eξ) = ind(Enξn) be an inductive limit of a sequence (Enξn)nN of locally convex spaces and let every step (Enξn) be endowed with a partial order by a pointed convex (solid) cone Sn. In the framework of inductive limits of partially ordered locally convex spaces, the notions of lastingly efficient points, lastingly weakly efficient points and lastingly globally properly efficient points are introduced. For several ordering cones, the notion of non-conflict is introduced. Under the requirement that the sequence (Sn)nN of ordering cones is non-conflicting, an existence theorem on lastingly weakly efficient points is presented. From this, an existence theorem on lastingly globally properly efficient points is deduced.

关键词: locally convex space, inductive limit, vector optimization, efficient point, weakly efficient point

Abstract:

Let (Eξ) = ind(Enξn) be an inductive limit of a sequence (Enξn)nN of locally convex spaces and let every step (Enξn) be endowed with a partial order by a pointed convex (solid) cone Sn. In the framework of inductive limits of partially ordered locally convex spaces, the notions of lastingly efficient points, lastingly weakly efficient points and lastingly globally properly efficient points are introduced. For several ordering cones, the notion of non-conflict is introduced. Under the requirement that the sequence (Sn)nN of ordering cones is non-conflicting, an existence theorem on lastingly weakly efficient points is presented. From this, an existence theorem on lastingly globally properly efficient points is deduced.

Key words: locally convex space, inductive limit, vector optimization, efficient point, weakly efficient point

中图分类号: 

  • 46A03