Conjugate gradient methods are well-known methods which are widely applied in many practical fields. CD conjugate gradient method is one of the classical types. In this paper, a modified three-term type CD conjugate gradient algorithm is proposed. Some good features are presented as follows: (i) A modified three-term type CD conjugate gradient formula is presented. (ii) The given algorithm possesses sufficient descent property and trust region property. (iii) The algorithm has global convergence with the modified weak Wolfe–Powell (MWWP) line search technique and projection technique for general function. The new algorithm has made great progress in numerical experiments. It shows that the modified three-term type CD conjugate gradient method is more competitive than the classical CD conjugate gradient method.

中文翻译：

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求解无约束优化问题的改进的三项式CD共轭梯度算法

共轭梯度法是在许多实际领域中广泛应用的众所周知的方法。CD共轭梯度法是经典类型之一。本文提出了一种改进的三项式CD共轭梯度算法。呈现出一些良好的特征，如下：（i）提出了一种改进的三项式CD共轭梯度公式。（ii）给定算法具有足够的下降特性和信任区域特性。（iii）该算法通过改进的弱Wolfe-Powell（MWWP）线搜索技术和通用函数投影技术具有全局收敛性。新算法在数值实验中取得了很大进展。结果表明，改进的三项式CD共轭梯度法比经典的CD共轭梯度法更具竞争力。