数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (4): 1154-1166.doi: 10.1016/S0252-9602(10)60113-0

• 论文 • 上一篇    下一篇

SEPARABLE CONDITIONS AND SCALARIZATION OF BENSON PROPER EFFICIENCY

丘京辉, 郝媛, 王璀   

  1. Department of Mathematics, Suzhou University, Suzhou 215006, China
  • 收稿日期:2007-09-07 修回日期:2008-08-11 出版日期:2010-07-20 发布日期:2010-07-20
  • 基金资助:

    Supported by the National Natural Science Foundation of China (10571035, 10871141)

SEPARABLE CONDITIONS AND SCALARIZATION OF BENSON PROPER EFFICIENCY

 QIU Jing-Hui, HAO Yuan, WANG Cui   

  1. Department of Mathematics, Suzhou University, Suzhou 215006, China
  • Received:2007-09-07 Revised:2008-08-11 Online:2010-07-20 Published:2010-07-20
  • Supported by:

    Supported by the National Natural Science Foundation of China (10571035, 10871141)

摘要:

Under the assumption that the ordering cone has a nonempty interior and is separable (or the feasible set has a
nonempty interior and is separable), we give scalarization theorems on Benson proper efficiency. Applying the results to vector optimization problems with nearly cone-subconvexlike set-valued maps, we obtain scalarization theorems and Lagrange multiplier theorems for Benson proper efficient solutions.

关键词: Locally convex space, nearly cone-subconvexlike set-valued map, Benson proper efficiency, scalarization

Abstract:

Under the assumption that the ordering cone has a nonempty interior and is separable (or the feasible set has a
nonempty interior and is separable), we give scalarization theorems on Benson proper efficiency. Applying the results to vector optimization problems with nearly cone-subconvexlike set-valued maps, we obtain scalarization theorems and Lagrange multiplier theorems for Benson proper efficient solutions.

Key words: Locally convex space, nearly cone-subconvexlike set-valued map, Benson proper efficiency, scalarization

中图分类号: 

  • 90C29