Benson真有效意义下向量集值优化的广义Fritz John条件

盛宝怀; 刘三阳

Benson真有效意义下向量集值优化的广义Fritz John条件

盛宝怀^1,2,
刘三阳¹

1.
西安电子科技大学应用数学系, 西安 710071;
2.
宁波大学数学研究所, 浙江宁波 315211

基金项目: 国家自然科学基金资助项目(69972036);宁波市博士基金资助项目;宁波大学博士后基金资助项目

详细信息

作者简介:
盛宝怀(1962- ),男,陕西凤县人,副教授,博士(E-mail:shengbaohuai@263.net).

中图分类号: O221.6
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- 文章访问数: 2530
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- 被引次数: 0
出版历程
- 收稿日期: 2000-03-29
- 修回日期: 2002-05-14
- 刊出日期: 2002-12-15

On the Generalized Fritz John Optimality Conditions of Vector Optimization With Set-Valued Maps Under Benson Proper Efficiency

SHENG Bao-huai^1,2,
LIU San-yang¹

1.
Department of Applied Mathematics, Xidian University, Xi'an 710071, P R China;
2.
Institute of Mathematics, Ningbo University, Ningbo, Zhejiang 315211, P R China

摘要

摘要: 引入了一种有关集值映射的切导数和强、弱*伪凸的概念。借助凸集分离定理及锥分离定理建立了Benson真有效意义下向量集值优化导数型的FritzJohn最优性条件,并对条件的充分性进行了讨论。当特殊到单值映射时这些最优性条件与经典的结果完全吻合。
- Contingent切锥 /
- 集值映射 /
- Benson真有效 /
- Fritz John条件
Abstract: A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condition of set-valued optimization under Benson proper efficiency is established,its sufficience is discussed. The form of the optimality conditions obtained here completely tally with the classical results when the set-valued map is specialized to be a single-valued map.
- Contingent tangent cone /
- set-valued map /
- Benson proper efficiency /
- Fritz John condition

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参考文献(15)

[1]	胡毓达.多目标规划有效性理论[M].上海:上海科学技术出版社,1994,126-127.
[2]	Luc D T.Theory of Vector Optimization,Lecture Notes in Economics and Mathematical Systems[M].Berlin:Springer-Verlag,1989:140-164.
[3]	Corley H W.Optimality conditions for maximizations of set-valued functions[J].J Optim Theory Appl,1988,58(1):1-10.
[4]	CHEN Guang-ya,Jahn J.Optimality conditions for set-valued optimization problems[J].Math Methods Oper Res,1998,48(2):187-200.
[5]	孟志青.集值映射的Hahn-Banach定理[J].应用数学和力学,1998,19(1):55-61.
[6]	Baier J,Jahn J.On subdifferential of set-valued maps[J].J Optim Theory Appl,1999,100(1):233-240.
[7]	WANG Shou-yang,LI Zhong-fei.Scalarization and Lagrange duality in multiobjective optimization[J].Optimization,1992,26(2):315-324.
[8]	CHEN Guang-ya,RONG Wei-dong.Characterizations of the Benson proper efficiency for nonconvex vector optimization[J].J Optim Theory Appl,1998,98(2):365-384.
[9]	LI Zhong-fei.Benson proper efficiency in the vector optimization of set-valued maps[J].J Optim Theory Appl,1998,98(3):623-649.
[10]	盛宝怀,刘三阳,熊胜君.Benson 真有效意义下向量集值优化的广义Fritz John条件[J].经济数学,2000,17(1):59-65.
[11]	Aubin J P,Frankowska H.Set-Valued Analysis[M].Boston:Birkhauser,1990,121-138.
[12]	Borwein J M.Proper efficient points for maximizations with respect to cone[J].SIAM J Control Optim,1977,15(1):57-63.
[13]	LI Ze-min.A theorem of the alternative and its application to the optimization of set-valued maps[J].J Optim Theory Appl,1999,100(2):365-375.
[14]	Dauer J P,Saleh O A.A characterization of proper minimal problem as a solutions of sublinear optimization problems[J].J Math Anal Appl,1993,178(2):227-246.
[15]	Zowe J.A remark on a regularity assumption for the mathematical programming problem in Banach spaces[J].J Optim Theory Appl,1978,25(3):375-381.