| 在集优化意义下的集值映射的非线性标量化 |
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| 引用本文： | 任创业,薛小维. 在集优化意义下的集值映射的非线性标量化[J]. 四川大学学报(自然科学版), 2013, 50(3): 441-446 |
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| 作者姓名： | 任创业 薛小维 |
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| 作者单位： | 重庆大学数学与统计学院,重庆,401331 |
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| 基金项目： | 国家自然科学基金(11171362);中央高校基本科研业务费(CDJXS12100022) |
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| 摘 要： | 本文研究了一个在集合序下的集值映射优化问题.为得到在这种集合序下的集优化问题的一些最优性条件,我们引入了一个非线性标量化函数,并研究了该函数的一些性质.通过这个非线性标量化函数,在没有任何凸性假设前提下,我们获得了这种集优化问题的标量化表示.作为应用我们还得到了一个存在性定理.
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| 关 键 词： | 集优化 非线性标量化函数 存在性定理 最优性条件 |
| 收稿时间： | 2012-11-18 |
Nonlinear scalarization in set optimization with set valued maps |
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| REN Chuang-Ye and XUE Xiao-Eei. Nonlinear scalarization in set optimization with set valued maps[J]. Journal of Sichuan University (Natural Science Edition), 2013, 50(3): 441-446 |
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| Authors: | REN Chuang-Ye and XUE Xiao-Eei |
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| Affiliation: | College of Mathematics and Statistics, Chongqing University;College of Mathematics and Statistics, Chongqing University |
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| Abstract: | In this paper, a set optimization problem with set valued maps is studied. A nonlinear scalarization function is introduced. Some properties of the function is discussed. By virtue of the nonlinear scalarization function, some optimization conditions for the set optimization problem are obtained. The scalar representations of set optimization problems is obtained without any convexity assumption. As an application, an existence theorem is also obtained. |
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| Keywords: | set optimization nonlinear scalarization function existence theorem optimization condition |
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