锥约束非光滑多目标优化问题的对偶及最优性条件

Acta mathematica scientia,Series A ›› 2012, Vol. 32 ›› Issue (1): 1-12.

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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

Abstract

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

CLC Number:

90C29

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

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