A descent modified Polak–Ribière–Polyak conjugate gradient method and its global convergence
A descent modified Polak–Ribière–Polyak conjugate gradient method and its global convergence
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DOI：
10.1093/imanum/drl016
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发表时间：
2006-10
影响因子：
2.1
通讯作者：
Li Zhang;W. Zhou;Donghui Li
中科院分区：
文献类型：
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作者：
Li Zhang;W. Zhou;Donghui Li
本文提出了一种改进的Polak-Ribiere-Polyak（PRP）共轭梯度法。所提出的方法的一个吸引人的性质是，由该方法产生的方向总是一个下降方向的目标函数。此属性与所使用的行搜索无关。如果采用精确线搜索，则该方法退化为普通PRP方法。在适当的条件下，我们证明了修正的PRP方法与Armijo型线搜索是全局收敛的。我们还提出了广泛的初步数值实验，以显示所提出的方法的效率。
In this paper, we propose a modified Polak-Ribiere-Polyak (PRP) conjugate gradient method. An attractive property of the proposed method is that the direction generated by the method is always a descent direction for the objective 'function. This property is independent of the line search used. Moreover, if exact line search is used, the method reduces to the ordinary PRP method. Under appropriate conditions, we show that the modified PRP method with Armijo-type line search is globally convergent. We also present extensive preliminary numerical experiments to show the efficiency of the proposed method.