In this paper, we propose a hybrid conjugate gradient (CG) method based on the approach of convex combination of Fletcher–Reeves (FR) and Polak–Ribière–Polyak (PRP) parameters, and Quasi-Newton’s update. This is made possible by using self-scaling memory-less Broyden’s update together with a hybrid direction consisting of two CG parameters. However, an important property of the new algorithm is that, it generates a descent search direction via non-monotone type line search. The global convergence of the algorithm is established under appropriate conditions. Finally, numerical experiments on some benchmark test problems, demonstrate the effectiveness of the proposed algorithm over some existing alternatives.

在本文中，我们基于Fletcher-Reeves（FR）和Polak-Ribière-Polyak（PRP）参数的凸组合方法和拟牛顿更新方法，提出了一种混合共轭梯度（CG）方法。通过使用无标度的无内存Broyden更新以及由两个CG参数组成的混合方向，可以实现这一点。然而，新算法的一个重要特性是，它通过非单调类型线搜索生成了下降搜索方向。在适当条件下建立算法的全局收敛性。最后，通过一些基准测试问题的数值实验，证明了该算法在某些现有替代方案上的有效性。