| 同伦方法求解无约束非凸优化问题的局部极小 |
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| 引用本文： | 孙文娟,李忠范,王彩玲,王明明.同伦方法求解无约束非凸优化问题的局部极小[J].东北师大学报(自然科学版),2009,41(3). |
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| 作者姓名： | 孙文娟 李忠范 王彩玲 王明明 |
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| 作者单位： | 孙文娟(沈阳理工大学理学院,辽宁,沈阳,110168);李忠范,王彩玲(吉林大学数学学院,吉林,长春,130012);王明明(空军航空大学数学教研室,吉林,长春,130022) |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 利用同伦方法求解无约束非凸优化问题,证明了在同伦映射为正则映射的条件下,选取合适的同伦方程,当算法可以排除鞍点时,同伦方法一定收敛到局部极小解,而非极大解.
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| 关 键 词： | 无约束非凸优化 同伦方法 局部极小 |
Homotopy method for getting a local minimum of unconstrained non-convex programming |
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| SUN Wen-juan,LI Zhong-fan,WANG Cai-ling,WANG Ming-ming.Homotopy method for getting a local minimum of unconstrained non-convex programming[J].Journal of Northeast Normal University (Natural Science Edition),2009,41(3). |
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| Authors: | SUN Wen-juan LI Zhong-fan WANG Cai-ling WANG Ming-ming |
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| Institution: | SUN Wen-juan1,LI Zhong-fan2,WANG Cai-ling2,WANG Ming-ming3(1.School of Science,Shenyang Ligong University,Shenyang 110168,China,2.College of Mathematics,Jilin University,Changchun 130012,3.Teaching , Research Section of,Mathematics The Aviation University of Air Force,Changchun 130022,China) |
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| Abstract: | In this paper,a homotopy method is used to solve unconstrained nonconvex programming problems.It proves that,when the homotopy map is a regular map,after are saddle points eliminated in the homotopy algorithm,it must converge to a local minimum by choosing proper homotopy equation. |
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| Keywords: | unconstrained nonconvex programming homotopy mehod local minimum |
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