| 引用本文： |
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陆莎,韦增欣,袁功林.基于三次模型的线搜索方法及其收敛性[J].广西科学,2010,17(3):209-211. [点击复制]
- LU Sha,WEI Zeng-xin,YUAN Gong-lin.A Line Search Method with Cubic Model and It's Convergence Property[J].Guangxi Sciences,2010,17(3):209-211. [点击复制]
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| 摘要: |
| 针对无约束优化问题,给出一种基于三次模型的线搜索型算法,并在适当的条件下证明算法的全局收敛性.该算法以对称矩阵代替原三次模型中的Hessian阵,并且不需要保持正定和Dennis-Moré条件,它与一般线搜索法不同,在每次迭代中步长可以在下降方向上由显性公式直接确定,从而可以减少搜索计算. |
| 关键词: 三次模型 线搜索 无约束优化 全局收敛 |
| DOI： |
| 投稿时间：2010-06-09 |
| 基金项目:国家自然科学基金项目(10761001),广西自然科学基金项目(0991028),广西大学科研基金项目(X081082)资助。 |
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| A Line Search Method with Cubic Model and It's Convergence Property |
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LU Sha1, WEI Zeng-xin2, YUAN Gong-lin2
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| (1.School of Mathematical Science, Guangxi Teachers Education University, Nanning, Guangxi, 530023, China;2.School of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, China) |
| Abstract: |
| A line search method with conic model for unconstrained optimization was proposed, and its global convergence result was proved under some suitable conditions. In the cubic model of the algorithm, the Hessian matrix of the objective function is replaced by a symmetric matrix without the positive definite assumption and the Dennis-Moré condition. At each iteration, the step-size is computed by an explicit formula on the descent direction which is different from general line search methods so that the search computation can be simplified. |
| Key words: cubic model line search method unconstrained optimization global convergence |
