| 集值优化问题严有效元的标量化刻画 |
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| 引用本文： | 徐义红.集值优化问题严有效元的标量化刻画[J].苏州科技学院学报(自然科学版),2003,20(4):5-8. |
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| 作者姓名： | 徐义红 |
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| 作者单位： | 南昌大学,基础部,江西,南昌,330029;西安电子科技大学,应用数学系,陕西,西安,710071 |
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| 基金项目： | 国家自然科学基金69972036。 |
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| 摘 要： | 在Hausdorff局部凸拓扑线性空间中考虑约束集值优化问题(VP)在严有效性意义下的标量化问题，给出了VP在严有效性意义下的一种等价刻画。
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| 关 键 词： | 严有效性 近似锥-次类凸 集值优化 锥 标量化 拓扑线性空间 拉格朗日对偶定理 |
| 文章编号： | 1672-0687(2003)04-0005-04 |
| 修稿时间： | 2003年2月25日 |
A Scalar Characterization on Strictly Efficient Elements in Set-Valued Optimization |
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| XU Yi-hong.A Scalar Characterization on Strictly Efficient Elements in Set-Valued Optimization[J].Journal of University of Science and Technology of Suzhou,2003,20(4):5-8. |
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| Authors: | XU Yi-hong |
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| Institution: | XU Yi-hong,Department of Basic Sciences,Nanchang University,Nanchang330029,China,Department of Applied Mathematics,Xidian University,Xi'an710071,China) |
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| Abstract: | The set-valued optimization problem with constraints VP is considered in the sense of strict efficiency in Hausdorff locally convex and topological linear spaces.Under the assumption of the approximate cone subconvex for the objective function,by applying separation theorem for con-vex sets,a necessary condition is derived for VP to attain its strictly efficient element.With the properties of the base functional,a sufficient condition is also presented.Finally,a characterization equivalent to VP is given in the sense of strict efficiency. |
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| Keywords: | strict efficiency approximate cone subconvex set-valued optimization cone |
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