| 集值优化问题强有效元的二阶最优性条件 |
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| 引用本文： | 孙鑫,徐义红,汪涛. 集值优化问题强有效元的二阶最优性条件[J]. 吉林大学学报(理学版), 2011, 49(5): 861-864 |
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| 作者姓名： | 孙鑫 徐义红 汪涛 |
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| 作者单位： | 南昌大学 数学系, 南昌 330031 |
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| 基金项目： | 国家自然科学基金(批准号:10461007); 江西省自然科学基金(批准号:2009GZS0021); 江西省教育厅科技项目(批准号:GJJ09069) |
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| 摘 要： | 在实赋范线性空间中考虑集值优化问题的强有效性, 借助集值映射的二阶切导数, 利用基泛函及强有效元的性质, 给出了目标函数为近似锥次类凸时无约束集值优化问题的二阶导数型最优性的必要条件, 并在锥 凸假设下给出了充分条件.
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| 关 键 词： | 集值优化 二阶切导数 强有效元 |
| 收稿时间： | 2010-12-14 |
Second-Order Optimality Conditions for Strong Efficient Element of Set-Valued Optimization |
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| SUN Xin,XU Yi-hong,WANG Tao. Second-Order Optimality Conditions for Strong Efficient Element of Set-Valued Optimization[J]. Journal of Jilin University: Sci Ed, 2011, 49(5): 861-864 |
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| Authors: | SUN Xin XU Yi-hong WANG Tao |
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| Affiliation: | Department of Mathematics, Nanchang University, Nanchang 330031, China |
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| Abstract: | The strong efficiency of set-valued optimization in real normed spaces was solved by applying the second-order contingent derivatives,the properties of basic functional and strong efficient element.The second-order necessary optimality condition of unconstrained set-valued optimization was given for the objective function being nearly cone-subconvexlike,and sufficient condition was presented under cone-convexity hypothesis. |
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| Keywords: | set-valued optimization second-order contingent derivative strong efficient element |
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