| 集值优化问题ε-强有效元的Lagrange型最优性条件 |
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| 引用本文： | 徐义红,韩倩倩,汪涛,吕强.集值优化问题ε-强有效元的Lagrange型最优性条件[J].山东大学学报(理学版),2013,48(3):80-83. |
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| 作者姓名： | 徐义红 韩倩倩 汪涛 吕强 |
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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： | 国家自然科学基金资助项目(10461007);江西省自然科学基金资助项目(20122BAB201003);江西省教育厅科技项目(GJJ12010) |
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| 摘 要： | 利用近似锥-次类凸集值映射的性质证明了当序偶集值映射是近似锥-次类凸时,对应的Lagrange函数也是近似锥-次类凸的。利用此结果得到集值优化问题取得ε 强有效元的Lagrange型必要条件,利用ε-强有效元的性质得到Lagrange型充分条件。
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| 关 键 词： | &epsilon -强有效元 近似锥-次类凸 集值优化 |
| 收稿时间： | 2012-10-22 |
Lagrange optimality conditions for set-valued optimization problem in the sense of ε-strongly efficient elements |
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| Institution: | Department of Mathematics, Nanchang University, Nanchang 330031, Jiangxi, China |
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| Abstract: | By applying properties of the nearly cone-subconvexlike set valued map, the result was proved that for a nearly cone-subconvexlike ordered pair set-valued map, its relevant Lagrange map is also nearly cone-subconvexlike. With help of such result, a Lagrange optimality necessary condition was established in the sense of ε-strongly efficiency. By taking advantage of properties of an ε-strongly efficient point, a Lagrange optimality sufficient condition was also obtained. |
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| Keywords: | &epsilon -strongly efficient element near cone-subconvexlikeness set-valued optimization |
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