| 一类多目标优化问题弱有效解的必要最优性条件 |
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| 引用本文： | 欧小庆,李金富,刘佳,廖霞,陈加伟.一类多目标优化问题弱有效解的必要最优性条件[J].西南农业大学学报,2018,40(10):107-111. |
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| 作者姓名： | 欧小庆 李金富 刘佳 廖霞 陈加伟 |
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| 作者单位： | 重庆人文科技学院管理学院;西南大学数学与统计学院 |
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| 基金项目： | 国家自然科学基金项目（11571055）；重庆市基础与前沿研究项目（cstc2016jcyjA0239，cstc2015jcyjBX0131）. |
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| 摘 要： | 标量化方法是研究多目标优化问题的最优性条件与算法的重要手段,最优性理论是优化理论的重要研究内容之一.建立了一类标量化函数的相关性质,并借助标量化技巧与Clarke次微分,在假设次微分约束规格成立的条件下,建立了一类非光滑多目标优化问题的局部弱有效解的Karush-Kuhn-Tucker必要最优性条件.
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| 关 键 词： | 多目标优化 局部弱有效解 必要最优性条件 约束规格 |
| 收稿时间： | 2017/9/4 0:00:00 |
Necessary Optimality Conditions for a Class of Nonsmooth Constrained Multiobjective Optimization Problems |
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| OU Xiao-qing,LI Jin-fu,LIU Ji,LIAO Xi,CHEN Jia-wei.Necessary Optimality Conditions for a Class of Nonsmooth Constrained Multiobjective Optimization Problems[J].Journal of Southwest Agricultural University,2018,40(10):107-111. |
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| Authors: | OU Xiao-qing LI Jin-fu LIU Ji LIAO Xi CHEN Jia-wei |
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| Institution: | 1. College of Management, Chongqing College of Humanities, Science & Technology, Chongqing 401524, China;2. School of Mathematics and Statistics, Southwest University, Chongqing 400715, China |
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| Abstract: | The scalarization method is an important means for the study of optimality and algorithms of multi-objective optimization problems, and optimality theory is one of the important contents in the optimization theory. In this paper, we first establish some properties of a class of scalarization functions. Then, with the scalarization method and Clarke subdifferentials, we establish the Karush-Kuhn-Tucker necessary optimality conditions for the local weakly efficient solution of a nonsmooth constrained multi-objective optimization problem under the assumption of subdifferential constraint qualification. |
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| Keywords: | multiobjective optimization local weakly efficient solution necessary optimality condition constraint qualification |
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