To find a solution of unconstrained optimization problems, we normally use a conjugate gradient (CG) method since it does not cost memory or storage of second derivative like Newton’s method or Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. Recently, a new modification of Polak and Ribiere method was proposed with new restart condition to give a so-call AZPRP method. In this paper, we propose a new modification of AZPRP CG method to solve large-scale unconstrained optimization problems based on a modification of restart condition. The new parameter satisfies the descent property and the global convergence analysis with the strong Wolfe-Powell line search. The numerical results prove that the new CG method is strongly aggressive compared with CG_Descent method. The comparisons are made under a set of more than 140 standard functions from the CUTEst library. The comparison includes number of iterations and CPU time.

中文翻译：

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大规模无约束优化问题的一种改进的AZPRP共轭梯度法

为了找到无约束优化问题的解决方案，我们通常使用共轭梯度（CG）方法，因为它不会像牛顿方法或Broyden–Fletcher–Goldfarb–Shanno（BFGS）方法那样消耗内存或存储二阶导数。最近，有人提出了对Polak和Ribiere方法的新修改，并以新的重启条件给出了所谓的AZPRP方法。在本文中，我们提出了一种新的AZPRP CG方法改进方法，它基于重新启动条件的改进方法来解决大规模无约束优化问题。通过强大的Wolfe-Powell线搜索，新参数满足了下降特性和全局收敛性分析。数值结果证明，与CG_Descent方法相比，新的CG方法具有较强的攻击性。比较是根据CUTEst库中的140多个标准函数进行的。比较包括迭代次数和CPU时间。