一种下降的混合共轭梯度法

A Descent Hybrid Conjugate Gradient Method

对于非线性共轭梯度法,文章在前人提出的混合共轭梯度法基础上,提出一种新的混合共轭梯度法,证明它的全局收敛性,并用新的公式建立算法框架.在不依赖任何线性搜索条件的情况下,证明算法框架生成的迭代方向满足充分下降条件,并在标准Wolfe线搜索条件下证明算法的全局收敛性.对新算法进行数值试验,结果表明改进后的算法是有效的.

For the nonlinear conjugate gradient method,a new hybrid conjugate gradient method is proposed based on the hybrid conjugate gradient method proposed by Jiang Xianzhen et al.The global convergence of the hybrid conjugate gradient method is proved,and the algorithm framework is established by using the new formula.It is proved that the iterative direction generated by the algorithm framework satisfies the sufficient descent condition,and the global convergence of the algorithm is proved under the standard Wolfe line search condition.Finally,numerical experiments are carried out on the new algorithm,and the results show that the improved algorithm is effective.