集值优化强有效解的广义二阶锥方向导数刻画 |
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引用本文: | 徐义红,孙鑫,汪涛.集值优化强有效解的广义二阶锥方向导数刻画[J].运筹学杂志,2013(4):80-86. |
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作者姓名: | 徐义红 孙鑫 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(No.61175127);江西省自然科学基金(No.20122BAB201003);江西省教育厅科技基金(No.GJJ12010) |
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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Henig扩张锥和基泛函的性质,利用广义二阶锥方向相依导数,得到受约束于集值映射的优化问题,取得强有效元的二阶最优性必要条件.当目标函数为近似锥一次类凸映射时,利用强有效点的标量化定理,得到集值优化问题,取得强有效元的二阶充分条件.
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关 键 词: | 强有效性 广义二阶锥方向相依导数 集值优化 |
Characterizations on strongly efficient solutions of set-valued optimization with generalized second-order cone-directed derivatives |
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Authors: | XU Yihong SUN Xin WANG Tao |
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Institution: | 1. Department of Mathematics, Nanchang University, Nanchang 330031, China |
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Abstract: | The strong efficiency for set-valued optimization is considered in real normed spaces. With the help of the properties of Henig dilating cone and base functional, by applying generalized second-order cone-directed contingent derivates, a second-order optimality necessary condition is established for a pair to be a strongly efficient element of set-valued optimization whose constraint condition is determined by a set-valued mapping. When objective function is nearly cone-subconvexlike, with the scalarization theorem for a strongly efficient point an a pair to be a strongly efficient element optimality sufficient condition is also derived for of set-valued optimization. |
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Keywords: | strong efficiency generalized second-order cone-directed contingent derivate set-valued optimization |
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