用广义高阶锥方向邻接导数刻画集值优化的超有效解

J4 ›› 2012, Vol. 50 ›› Issue (06): 1146-1150.

用广义高阶锥方向邻接导数刻画集值优化的超有效解

韩倩倩, 徐义红, 汪涛, 涂相求

南昌大学数学系, 南昌 330031

收稿日期:2011-12-30 出版日期:2012-11-26 发布日期:2012-11-26
通讯作者: 徐义红 E-mail:xuyihong@ncu.edu.cn

Super Efficient Solutions of Set-Valued Optimization with Generalized HigherOrder ConeDirected Adjacent Derivatives

HAN Qianqian, XU Yihong, WANG Tao, TU Xiangqiu

Department of Mathematics, Nanchang University, Nanchang 330031, China

Received:2011-12-30 Online:2012-11-26 Published:2012-11-26
Contact: XU Yihong E-mail:xuyihong@ncu.edu.cn

摘要/Abstract

摘要：

在赋范线性空间中利用广义高阶锥方向邻接导数研究集值优化问题的超有效解. 在近似锥次类凸假设下, 借助凸集分离定理和Henig扩张锥的性质, 得到了集值优化问题取得超有效元的Fritz John型必要条件.

关键词: 超有效解, 广义m阶C方向邻接导数, 集值优化

Abstract:

In normed linear spaces, the super efficient solutions of set-valued optimization were investigated with generalized higherorder conedirected adjacent derivatives. Under the assumption of near conesubconvexlikeness, with the help of separate theorem for convex sets and the properties of Henig
dilating cone, the type of Fritz John necessary optimality condition was established for setvalued optimization problem to obtain its super efficient elements.

Key words: super efficient solution, conedirected mth-order generalized adjacent derivative, setvalued optimization

中图分类号:

O221.6

韩倩倩, 徐义红, 汪涛, 涂相求. 用广义高阶锥方向邻接导数刻画集值优化的超有效解[J]. J4, 2012, 50(06): 1146-1150.

HAN Qian-Qian, XU Xi-Gong, HONG Chao, CHU Xiang-Qiu. Super Efficient Solutions of Set-Valued Optimization with Generalized HigherOrder ConeDirected Adjacent Derivatives[J]. J4, 2012, 50(06): 1146-1150.

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