## 留言板

Benson真有效意义下向量集值优化的广义Fritz John条件

 引用本文: 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[J]. 应用数学和力学, 2002, 23(12): 1289-1295.
SHENG Bao-huai, LIU San-yang. On the Generalized Fritz John Optimality Conditions of Vector Optimization With Set-Valued Maps Under Benson Proper Efficiency[J]. Applied Mathematics and Mechanics, 2002, 23(12): 1289-1295.
 Citation: SHENG Bao-huai, LIU San-yang. On the Generalized Fritz John Optimality Conditions of Vector Optimization With Set-Valued Maps Under Benson Proper Efficiency[J]. Applied Mathematics and Mechanics, 2002, 23(12): 1289-1295.

## Benson真有效意义下向量集值优化的广义Fritz John条件

###### 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

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

• 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。
•  [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.
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##### 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

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