| 解无约束优化问题的一个新的带线搜索的信赖域算法 |
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| 引用本文： | 刘景辉,马昌凤,陈争.解无约束优化问题的一个新的带线搜索的信赖域算法[J].计算数学,2012,34(3):275-284. |
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| 作者姓名： | 刘景辉 马昌凤 陈争 |
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| 作者单位： | 1. 福建师范大学数学与计算机科学学院, 福州 350007;
2. 福建江夏学院信息系, 福州 350108 |
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| 摘 要： | 在传统信赖域方法的基础上, 提出了求解无约束最优化问题的一个新的带线搜索的信赖域算法. 该算法采用大步长 Armijo 线搜索技术获得迭代步长, 克服了每次迭代求解信赖域子问题时计算量较大的缺点, 因而适用于求解大型的优化问题. 在适当的条件下, 我们证明了算法的全局收敛性. 数值实验结果表明本文所提出的算法是有效的.
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| 关 键 词： | 无约束优化问题 信赖域方法 大步长 Armijo 线搜索 全局收敛性 |
| 收稿时间： | 2011-08-19; |
A TRUST REGION ALGORITHM WITH NEW LINE SEARCH FOR SOLVING UNCONSTRAINED OPTIMIZATION PROBLEMS |
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| Liu Jinghui
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Ma Changfeng
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Chen Zheng.A TRUST REGION ALGORITHM WITH NEW LINE SEARCH FOR SOLVING UNCONSTRAINED OPTIMIZATION PROBLEMS[J].Mathematica Numerica Sinica,2012,34(3):275-284. |
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| Authors: | Liu Jinghui Ma Changfeng Chen Zheng |
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| Institution: | 1. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China;
2. Department of Information, Fujian jiangxia University, Fuzhou 350108, China |
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| Abstract: | Based on the traditional trust region method,a trust region algorithm with new line search is proposed for solving unconstrained optimization problems.The stepsize is obtained making use of larger Armijo line search rule.The proposed algorithm overcomes the shortcomings of large amount of calculation when solving the subproblem at each iteration, therefore,it is more attractive for large scale optimization problems.The global convergence of the algorithm is proved under suitable conditions.Some numerical results are reported, which shows that our algorithm is quite effective. |
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| Keywords: | unconstrained optimization problem trust region algorithm larger Armijo line search global convergence |
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