| 锥约束非光滑多目标优化问题的对偶及最优性条件 |
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| 引用本文： | 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(A辑),2012,32(1):1-12. |
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| 作者姓名： | 陈加伟 李军 王景南 |
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| 作者单位： | 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 |
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| 基金项目： | 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 |
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| 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.
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| 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 |
| 收稿时间： | 2009-10-08 |
| 修稿时间： | 2011-12-16 |
Optimality Conditions and Duality for Nonsmooth Multiobjective Optimization Problems with Cone Constraints |
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| CHEN Jia-Wei,LI Jun,WANG Jing-Nan.Optimality Conditions and Duality for Nonsmooth Multiobjective Optimization Problems with Cone Constraints[J].Acta Mathematica Scientia,2012,32(1):1-12. |
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| Authors: | CHEN Jia-Wei LI Jun WANG Jing-Nan |
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| Institution: | 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 |
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| 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. |
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| Keywords: | Nonsmooth multiobjective optimization problemzz Saddle pointzz Generalizedcone-invex functionzz Weakly effcient solutionzz Weak (strong converse) dualityzz Kuhn-Tucker condi-tionzz |
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