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.
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 use the negative Newton direction as the search direction;if the Hessian matrix is singular or the scalar of the transposed vector of the gradient of the objective function and the Newton direction equals zero,we use the negative gradient as the search direction.So the search direction ensure that the objective function has always been a decline in direction.The algorithm is shown to converge globally.
出处
《闽江学院学报》
2009年第5期11-12,17,共3页
Journal of Minjiang University
关键词
修正
阻尼牛顿法
下降
全局收敛性
modified
damped Newton method
decline
global convergence.
