| 向量集值优化中的二次最优性条件 |
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| 引用本文： | 刘敬华,龚循华,何鸽.向量集值优化中的二次最优性条件[J].南昌大学学报(理科版),2007,31(2):103-109. |
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| 作者姓名： | 刘敬华 龚循华 何鸽 |
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| 作者单位： | 南昌大学,数学系,江西,南昌,330031 |
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| 基金项目： | 国家自然科学基金
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江西省自然科学基金 |
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| 摘 要： | 考虑集值向量优化中的二次最优性条件.引进了新的集值映射的二次切上导数概念,并利用这个概念给出了在无约束条件下弱有效点对,Henig有效点对,整体有效点对和f-有效点对的充分和必要条件,以及Benson有效点必要条件;还给出了有约束条件前四种有效点对的必要条件.
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| 关 键 词： | 集值向量优化 二次切上导数 最优性条件 向量集值优化 最优性条件 Optimization Vector 的必要条件 有约束条件 充分和必要条件 弱有效点 无约束 利用 导数概念 集值映射 集值向量优化 |
| 文章编号： | 1006-0464（2007）02-0103-07 |
| 修稿时间： | 2006-01-16 |
Second-order Optimality Conditions in Vector Set-valued Optimization |
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| LIU Jing-hua,GONG Xun-hua,He Ge.Second-order Optimality Conditions in Vector Set-valued Optimization[J].Journal of Nanchang University(Natural Science),2007,31(2):103-109. |
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| Authors: | LIU Jing-hua GONG Xun-hua He Ge |
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| Institution: | Department of Mathematics, Nanchang University, Nanchang 330031, China |
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| Abstract: | This paper considers second - order optimality conditions in vector set - valued optimization. It proposes new second - order epiderivatives for set - valued maps. By these concepts, it presents a few necessary and sufficient conditions for a weakly efficient solution, a Henig efficient solution, a global efficient solution, an f - efficient solution, respectively, to a vector set -valued optimizaition problem without constraints, and a necessary condition for a Benson efficient solution;moreover,it presents a few necessary conditions for a weakly efficient solution, a Henig efficient solution, a global efficient solution, an f-efficient solution, respectively, to a vector set -valued optimizaition problem with constraints. |
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| Keywords: | set - valued vector optimization second - order epiderivatives optimality conditions |
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