| 多目标最优化恰当有效解的稳定性 |
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| 引用本文： | 何莉敏,李德荣,侯玉双,王娟,李玉. 多目标最优化恰当有效解的稳定性[J]. 纯粹数学与应用数学, 2011, 27(1): 32-36 |
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| 作者姓名： | 何莉敏 李德荣 侯玉双 王娟 李玉 |
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| 作者单位： | 内蒙古科技大学数理与生物工程学院应用数学系,内蒙古,包头,014010 |
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| 基金项目： | 内蒙古教育厅高等学校科研项目，内蒙古科技大学教学研究重点项目 |
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| 摘 要： | 主要研究当两种类型的参数扰动时,多目标最优化问题中恰当有效解的稳定性.在点集映射的连续性意义下,分析讨论这种稳定性问题并分别给出引起扰动的两参数u,v所对应的点集映射Q1(u)和Q2(v),同时严格证明了在两个闭凸锥U,V上Q1(u)和Q2(v)的连续性定理.最后,通过附注对其进行补充和改进.
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| 关 键 词： | 多目标最优化 点集映射 上半连续 下半连续 恰当有效解 |
Stability of proper efficient solution for multi-objective optimization |
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| HE Li-min,LI De-rong,HOU Yu-shuang,WANG Juan,LI Yu. Stability of proper efficient solution for multi-objective optimization[J]. Pure and Applied Mathematics, 2011, 27(1): 32-36 |
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| Authors: | HE Li-min LI De-rong HOU Yu-shuang WANG Juan LI Yu |
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| Affiliation: | (School of Mathematics, Physics and Biological Engineering, Inner Mongolia University of Science andTechnological, Baotou 014010, China) |
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| Abstract: | This paper, the stability of the set of proper efficient solutions is studied with respect to two types of perturbation in multi-objective optimization problem. At the point-to-set mapping of the sense of continuity, the stability is analyzed and discussed, and two point-to-set mappings Q1（u） and Q2（v） with respectto u,v, respectively, are given. At the same time,the theorems of continuity of Q1（u） and Q2（v） are provedstrictly on condition that the domination structure are assumed to be two closed convex cones. Finally, some supplements and improvements are made by remarks. |
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| Keywords: | multi-objective optimization point-to-set mapping upper semi-continuous lower semi-continuous proper efficient solution |
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