锥约束非光滑多目标优化问题的对偶及最优性条件

数学物理学报 ›› 2012, Vol. 32 ›› Issue (1): 1-12.

• 论文 • 下一篇

锥约束非光滑多目标优化问题的对偶及最优性条件

陈加伟^1,3, 李军¹, 王景南²

1.西华师范大学数学与信息学院四川南充 637009;
2.明新科技大学财务金融系台湾新丰新竹 30401;
3.武汉大学数学与统计学院武汉 430072

收稿日期:2009-10-08 修回日期:2011-12-16 出版日期:2012-02-25 发布日期:2012-02-25
基金资助:
国家自然科学基金(60804065)、教育部科学技术研究重点项目(211163)、四川省青年科技基金、西华师范大学科研启动基金(08B075)、武汉大学博士研究生学术新人提名奖和中央高校基本科研业务费专项基金(20112010202004)资助

Optimality Conditions and Duality for Nonsmooth Multiobjective Optimization Problems with Cone Constraints

CHEN Jia-Wei^1,3, LI Jun¹, WANG Jing-Nan²

1. School of Mathematics and Information, China West Normal University, Sichuan Nanchong 637009;
2.Department of Finance, Minghsin University of Science and Technology, Taiwan Xinfeng Hsinchu 30401;
3.School of Mathematics and Statistics, Wuhan University, Wuhan 430072

Received:2009-10-08 Revised:2011-12-16 Online:2012-02-25 Published:2012-02-25
Supported by:
国家自然科学基金(60804065)、教育部科学技术研究重点项目(211163)、四川省青年科技基金、西华师范大学科研启动基金(08B075)、武汉大学博士研究生学术新人提名奖和中央高校基本科研业务费专项基金(20112010202004)资助

摘要/Abstract

摘要：

研究了一类涉广义不变凸锥约束非光滑多目标优化问题(记为(MOP)),结合Craven与Yang广义选择定理,建立了该优化问题的Kuhn-Tucker型最优性充分必要条件以及其鞍点与弱有效解之间的关系,给出了(MOP)的Wolfe型与Mond-Weir型弱、强以及逆对偶理论.

关键词: 非光滑多目标优化问题, 鞍点, 广义锥不变凸函数, 弱有效解, 弱(强、逆)对偶, Kuhn-Tucker型最优性条件

Abstract:

In this work, a nonsmooth multiobjective optimization problem involving gen-eralized invexity with cone constraints (for short, (MOP)) is considered. The Kuhn-Tucker necessary and su?cient conditions for (MOP) are established by using a generalized alterna-tive theorem of Craven and Yang. The relationship between saddle points and weakly effcient solutions of (MOP) is developed. Furthermore, the Wolfe type and Mond-Weir type weak, strong and converse duality results for (MOP) are presented. These results extend and improve
corresponding results of others.

Key words: Nonsmooth multiobjective optimization problem, Saddle point, Generalizedcone-invex function, Weakly effcient solution, Weak (strong, converse) duality, Kuhn-Tucker condi-tion

中图分类号:

90C29

陈加伟, 李军, 王景南. 锥约束非光滑多目标优化问题的对偶及最优性条件[J]. 数学物理学报, 2012, 32(1): 1-12.

CHEN Jia-Wei, LI Jun, WANG Jing-Nan. Optimality Conditions and Duality for Nonsmooth Multiobjective Optimization Problems with Cone Constraints[J]. Acta mathematica scientia,Series A, 2012, 32(1): 1-12.

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锥约束非光滑多目标优化问题的对偶及最优性条件

Optimality Conditions and Duality for Nonsmooth Multiobjective Optimization Problems with Cone Constraints

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