| 一个无约束有限内存信赖域方法及其实现 |
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| 引用本文： | 王周宏.一个无约束有限内存信赖域方法及其实现[J].计算数学,2005,27(4):395-404. |
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| 作者姓名： | 王周宏 |
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| 作者单位： | 中国科学院数学与系统科学院计算数学研究所,北京,100080;北京交通大学数学系,北京,100044 |
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| 基金项目： | 国家自然科学基金（10231060）和北京交通大学人才基金（LIJ05001）的资助项目 |
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| 摘 要： | 本文针对大规模无约束优化问题研究了一个新的有限内存信赖域实现方法,提出了一个在有限维（维数≤2m＋1）子空间上精确求解信赖域子问题的方法,大大减少了计算量;分析了方法的收敛性,并详细给出了数值计算方法,最后通过数值实验验证了方法的有效性.
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| 关 键 词： | 信赖域方法 大规模优化 有限内存方法 |
| 收稿时间： | 2004-07-16 |
| 修稿时间： | 2004-07-16 |
A LIMITED MEMORY TRUST REGION METHOD FOR UNCONSTRAINED OPTIMIZATION AND ITS IMPLEMENTATION |
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| Wang Zhouhong.A LIMITED MEMORY TRUST REGION METHOD FOR UNCONSTRAINED OPTIMIZATION AND ITS IMPLEMENTATION[J].Mathematica Numerica Sinica,2005,27(4):395-404. |
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| Authors: | Wang Zhouhong |
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| Institution: | Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Science, Chinese Academy of Science, Beijing 100080, China |
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| Abstract: | This paper gives a new way for the implementation of the limited memory quasi-Newton trust region methods for large scale unconstrained optimization. A method for solving the quadratic subproblem in a subspace whose dimension is at most 2m + 1 is given. The corresponding limited memory trust region algorithm is presented in detail and its convergence is analyzed. Numerical results for some typical large scale examples are reported and it shows that the new implementation is efficient. |
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| Keywords: | trust region methods large scale optimization limited memorymethods |
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