择一定理及向量优化问题的Benson真有效性

重庆交通大学学报（自然科学版） ›› 2006, Vol. 25 ›› Issue (4): 148-150.

择一定理及向量优化问题的Benson真有效性

王其林¹，刘军²，张健³

1.重庆交通学院基础部，重庆 400774；2.重庆师范大学化学学院，重庆 400047； 3.重庆师范大学数学与计算机科学学院，重庆 400047

收稿日期:2005-03-31 修回日期:2005-08-02 出版日期:2006-08-15 发布日期:2015-05-18
作者简介:王其林(1971—)，男，重庆丰都人，硕士，讲师，主要从事最优化理论及其应用的研究．
基金资助:
重庆交通学院科研基金资助课题(人才2004-02-20)资助

Alternative theorem and benson proper efi ciency for vector optimization problems

WANG Qi-1in ¹，LIU Jun²，ZHANG Jian³

1·Dept. of Basic Sciences，Chongqing Jiaotong University，Chongqing 400074 ， China；2.School of Chemistry，chongqing Normal University，Chongqing 400047，China；3.School of Mathematics＆ Computer Science. Chongqing Normal University，Chongqing 400047，China

Received:2005-03-31 Revised:2005-08-02 Online:2006-08-15 Published:2015-05-18

摘要/Abstract

摘要： 在局部凸Hausdorf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．

关键词: 近次似凸集值映射, 向量优化问题, 择一定理, Benson真有效性

Abstract: In this paper，nearly subeonvexlike set-valued maps were introduced and the alternative theorem under its was obtained in locally-onlvex Hamdorf spaces.Finally，a characterization of the benson proper efficiency for vector optimization problems of nearly subconverxlike set-valued maps Was obtained in terms of scalarization．

Key words: nearly subconvexlike set-valued maps, vector optimization problems, alternative theorem, Benson proper effciency

中图分类号:

O224

王其林，刘军，张健. 择一定理及向量优化问题的Benson真有效性[J]. 重庆交通大学学报（自然科学版）, 2006, 25(4): 148-150.

WANG Qi-1in，LIU Jun，ZHANG Jian. Alternative theorem and benson proper efi ciency for vector optimization problems[J]. Journal of Chongqing Jiaotong University(Natural Science), 2006, 25(4): 148-150.