| 非凸向量集值优化Benson真有效解的最优性条件与对偶 |
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| 引用本文： | 刘三阳,盛宝怀.非凸向量集值优化Benson真有效解的最优性条件与对偶[J].应用数学学报,2003,26(2):337-344. |
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| 作者姓名： | 刘三阳 盛宝怀 |
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| 作者单位： | 1. 西安电子科技大学应用数学系,西安,710071
2. 西南石油学院博士后流动站,南充,637001;宝鸡文理学院数学系,宝鸡,721007 |
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| 基金项目： | 国家自然科学基金(69972036号)，宁波市博士基金(02J20102-06号)，宁波大学博士后基金资助项目 |
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| 摘 要： | 在无需偏序锥内部非空的情况下给出了非凸约束向量集值优化Benaon真有效解一种加细的最优性条件，并建立了向量集值优化Benson真有效解一种改进的Lagrange乘子型对偶，它比已有的Lagrange乘子型对偶具有较好的对偶性。
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| 关 键 词： | Benson真有效解 非导数型最优性条件 Lagrange乘子型对偶 非凸向量集值优化 偏序锥 集值映射 上图 逆对偶定理 |
THE OPTIMALITY CONDITIONS AND DUALITY OF NONCONVEX VECTOR SET-VALUED OPTIMIZATION WITH BENSON PROPER EFFICIENCY |
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| LIU SANYANG.THE OPTIMALITY CONDITIONS AND DUALITY OF NONCONVEX VECTOR SET-VALUED OPTIMIZATION WITH BENSON PROPER EFFICIENCY[J].Acta Mathematicae Applicatae Sinica,2003,26(2):337-344. |
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| Authors: | LIU SANYANG |
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| Abstract: | A kind of refined optimality necessary and sufficient conditions for constrained vector optimization of set-valued maps with Benson proper efficient solutions is established without the assumption that the partial order cone's interior is nonempty, from which a modified Lagrangian duality for nonconvex vector optimization of set-valued maps with Benson proper efficient solutions is presented. The weak duality theorem, the direct duality theorem and the inverse duality theorem are given. The advantages of this kind of duality over the classical Lagrangian duality in the facts that it has better duality properties. |
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| Keywords: | Set-valued maps Benson proper efficiency optimality conditions duality |
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