| 一种改进的隐式Euler切线法 |
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| 引用本文： | 王希云,贾新辉,王子豪. 一种改进的隐式Euler切线法[J]. 应用数学和力学, 2017, 38(3): 347-354. DOI: 10.21656/1000-0887.370160 |
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| 作者姓名： | 王希云 贾新辉 王子豪 |
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| 作者单位： | 1太原科技大学 应用科学学院, 太原 030024;2复旦大学 数学科学学院, 上海 200433 |
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| 基金项目： | 山西省自然科学基金(2008011013)，山西省“131”领军人才工程项目 |
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| 摘 要： | 对于Hessian矩阵正定的情形，在求解二次函数模型信赖域子问题的隐式分段折线算法的基础上，提出一种求解信赖域子问题的改进的隐式Euler切线法，并分析该路径的性质.数值实验表明新算法是有效可行的，且较原算法具有迭代次数少、计算时间短等优点.
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| 关 键 词： | 隐式Euler切线法 信赖域子问题 微分方程模型 无约束优化 信赖域方法 |
| 收稿时间： | 2016-05-23 |
An Improved Implicit Eulerian Tangent Algorithm |
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| WANG Xi-yun,JIA Xin-hui,WANG Zi-hao. An Improved Implicit Eulerian Tangent Algorithm[J]. Applied Mathematics and Mechanics, 2017, 38(3): 347-354. DOI: 10.21656/1000-0887.370160 |
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| Authors: | WANG Xi-yun JIA Xin-hui WANG Zi-hao |
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| Affiliation: | 1School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, P.R.China;2School of Mathematical Sciences, Fudan University, Shanghai 200433, P.R.China |
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| Abstract: | Based on the implicit piecewise dogleg algorithm for solving trust region subproblems of quadratic models,and aimed at the condition that the Hessian matrix was positive deftnite,an improved implicit Eulerian tangent algorithm for solving trust region subproblems was presented.Then the nature of the path was analyzed.The numerical experiments show that the new algorithm is effective and practicable,and the advantages of the new algorithm compared with the previous algorithms lie in the smaller number of iterations,the shorter computing time and so on. |
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| Keywords: | implicit Eulerian tangent algorithm trust region subproblem differential equation model unconstrained optimization trust region method |
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