集值映射的广义梯度与超有效解

集值映射的广义梯度与超有效解

侯震梅^1,2, 周勇^1,2

1. 新疆财经学院统计与信息系, 乌鲁木齐 830012; 2. 西安电子科技大学应用数学系, 西安 710071

收稿日期:2005-01-24 修回日期:1900-01-01 出版日期:2006-01-26 发布日期:2006-01-26
通讯作者: 侯震梅

Generalized Gradient of Set-valued Mapping and Super-efficient Solution

HOU Zhen-mei^1,2, ZHOU Yong^1,2

1. Department of Statistics and Information, Xinjiang Institute of Finance and Economics, Urumqi 830012, China;2. Department of Applied Mathematics, Xidian University, Xi’an 710071, China

Received:2005-01-24 Revised:1900-01-01 Online:2006-01-26 Published:2006-01-26
Contact: HOU Zhen-mei

摘要/Abstract

摘要： 在锥序Banach空间中引入了一类集值映射的广义梯度，在一定条件下通过凸集分离定理证明了此广义梯度的存在性；并给出集值优化问题的超有效解在广义梯度下的最优条件.

关键词: 集值优化, 切导数, 超有效性, 广义梯度

Abstract: The generalized gradient of a kind of set-valued mappings is introduced into ordered Banach spaces and under certain conditions its existence is proved via the separation theorem. The optimality conditions of super-efficient solution of set-valued optimization problems are presented in the sense of generalized gradient.

Key words: set-valued optimization, contingent derivative, super-efficiency, generalized gradient

中图分类号:

O224

侯震梅, 周勇. 集值映射的广义梯度与超有效解[J]. J4, 2006, 44(01): 9-14.

HOU Zhen-mei, ZHOU Yong. Generalized Gradient of Set-valued Mapping and Super-efficient Solution[J]. J4, 2006, 44(01): 9-14.

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[3]	寇喜鹏, 彭兴媛, 朱胜坤. 约束集值优化问题的二阶最优性条件[J]. J4, 2012, 50(02): 244-250.
[4]	孙鑫, 徐义红, 汪涛. 集值优化问题强有效元的二阶最优性条件[J]. J4, 2011, 49(05): 861-864.
[5]	杨扬, 徐义红, 汪涛. 集值优化问题严有效解的高阶最优性条件[J]. J4, 2010, 48(05): 737-742.
[6]	肖明丽, 徐义红. 集值优化问题超鞍点的最优性条件[J]. J4, 2008, 46(05): 841-844.
[7]	肖刚, 刘三阳. 黎曼流形上非可微多目标规划的必要最优性条件[J]. J4, 2008, 46(02): 209-213.
[8]	余国林,, 刘三阳. 集值优化的严有效性和标量集值Lagrange映射[J]. J4, 2006, 44(06): 888-892.