| 一类修正阻尼牛顿算法 |
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| 引用本文： | 陈秀琴.一类修正阻尼牛顿算法[J].闽江学院学报,2009,30(5):11-12,17. |
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| 作者姓名： | 陈秀琴 |
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| 作者单位： | 闽江学院艺术系,福建福州350108 |
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| 摘 要： | 对一般目标函数极小化问题,提出一类新的修正阻尼牛顿法.若Hessian矩阵正定且目标函数梯度不为零,则搜索方向取牛顿方向;若Hessian矩阵不正定且非奇异,且目标函数梯度的转置和牛顿方向的数量积大于零时,搜索方向采用负牛顿方向;若Hessian矩阵奇异或者目标函数梯度的转置和牛顿方向的数量积等于零时,搜索方向则采用负梯度方向.因此该算法能保证搜索方向始终为下降方向,并证明对一般的非凸目标函数,该算法全局收敛.
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| 关 键 词： | 修正 阻尼牛顿法 下降 全局收敛性 |
An modified damped Newton method |
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| CHEN Xiu-qin.An modified damped Newton method[J].Journal of Minjiang University,2009,30(5):11-12,17. |
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| Authors: | CHEN Xiu-qin |
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| Institution: | CHEN Xiu-qin(Department of Art,Minjiang University,Fuzhou,Fujian 350108,China) |
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| Abstract: | In this paper,we propose a new modified damped Newton algorithm for solving the objective function minimization problems.In the algorithm,if the Hessian matrix of the objective function is positive definite and the gradient of the objective function doesn't equal zero,we use the Newton direction as the search direction;if the Hessian matrix is neither positive definite nor singular,and the scalar of the transposed vector of the gradient of the objective function and the Newton direction is more than zero,we... |
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| Keywords: | modified damped Newton method decline global convergence |
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