| 非凸集值优化弱有效解的广义最优性条件 |
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| 引用本文： | 王其林,张健.非凸集值优化弱有效解的广义最优性条件[J].四川师范大学学报(自然科学版),2011,34(2):181-185. |
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| 作者姓名： | 王其林 张健 |
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| 作者单位： | 1. 重庆交通大学,理学院,重庆,400074;重庆大学,数理学院,重庆,400044
2. 重庆市教育考试院,命题处,重庆,401147 |
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| 基金项目： | 国家自然科学基金，重庆市教委科研基金 |
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| 摘 要： | 在赋范空间中引入了集值映射的广义m-阶相依(邻接)导数.在没有任何凸性假设下,利用非线性标量化泛函和广义m-阶相依(邻接)导数,获得了无约束集值优化问题弱有效解的最优性必要和充分性条件,所获得的结果推广了文献中的几个结果.
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| 关 键 词： | 非凸集值优化 广义m-阶相依(邻接)导数 非线性标量化泛函 最优性条件 |
Generalized Optimality Conditions for Weakly Efficient Solutions in Nonconvex Set-valued Optimization |
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| WANG Qi-lin,ZHANG Jian.Generalized Optimality Conditions for Weakly Efficient Solutions in Nonconvex Set-valued Optimization[J].Journal of Sichuan Normal University(Natural Science),2011,34(2):181-185. |
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| Authors: | WANG Qi-lin ZHANG Jian |
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| Institution: | 1.College of Sciences,Chongqing Jiaotong University,Chongqing 400074; 2.College of Mathematics and Physics,Chongqing University,Chongqing 400044; 3.Section for Test Design,Chongqing Education Examinations Authority,Chongqing 401147) |
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| Abstract: | In this paper,the concepts of generalized contingent and adjacent derivatives of m-order are defined for set-valued maps in a real normaed space.By using these concepts and nonlinear scalarization fuctionals,we obtain some necessary and sufficient conditions for weakly efficient solutions of unconstrained set-valued optimization problems to be optimum in which there is no any convexity assumption.The results obtained in this paper generalize some others in recent literature. |
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| Keywords: | nonconvex set-valued optimization generalized contingent(adjacent) derivatives of m-order nonlinear scalarization functional optimality conditions |
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