| 非线性参数规划问题$\varepsilon$-最优解集集值映射的连续性 |
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| 引用本文： | 霍永亮.非线性参数规划问题$\varepsilon$-最优解集集值映射的连续性[J].系统科学与数学,2009,29(6):735-741. |
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| 作者姓名： | 霍永亮 |
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| 作者单位： | (1)重庆文理学院数学与统计学院, 永川 402160; (2)西安电子科技大学应用数学系, 西安 710071. |
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| 摘 要： | 对非线性参数规划问题$\varepsilon$-最优解集集值映射的连续性条件进行了研究.首先在可行集集值映射局部有界且正则的条件下,讨论了非线性参数规划问题最优值函数的连续性,然后针对$\varepsilon$-最优解集集值映射的结构特征并利用此结果和集值分析理论,给出了非线性参数规划问题$\varepsilon$-最优解集集值映射连续的一个充分条件.
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| 关 键 词： | 非线性参数规划 最优值函数 $\varepsilon$-最优解集 正则条件 连续性. |
| 收稿时间： | 2007-11-7 |
| 修稿时间： | 2008-9-8 |
The Continuity of $\varepsilon$-Optimal Solution Set Set-Valued Mapping in Nonlinear Parametric Programming Problem |
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| HUO Yongliang,LIU Sanyang.The Continuity of $\varepsilon$-Optimal Solution Set Set-Valued Mapping in Nonlinear Parametric Programming Problem[J].Journal of Systems Science and Mathematical Sciences,2009,29(6):735-741. |
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| Authors: | HUO Yongliang LIU Sanyang |
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| Institution: | (1)College of Mathematical and Statistics, Chongqing University of Arts and Sciences, Chongqing 402160; (2)Department of Applied Mathematics, XidianUniversity, Xi'an 710071. |
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| Abstract: | The continuity of $\varepsilon$-optimal solution set set-valued mapping in nonlinear parametric programming problem is considered. Firstly, the continuity of optimal value function in nonlinear parametric programming is discussedunder the locally bounded and regularity condition of feasible set set-valued mapping. Then based on the construction characteristic of $\varepsilon$-optimalsolution set set-valued mapping, a sufficient condition of continuity of $\varepsilon$-optimal solution set set-valued mapping for nonlinear parametric programming is obtained. |
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| Keywords: | Nonlinear parametric programming optimal value function $\varepsilon$-optimal solution set regularity condition continuity |
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