Recently, Jian, Han and Jiang proposed a descent hybrid conjugate gradient method which is globally convergent without convexity assumption on the objective function, being also sensibly promising in computational point of view. Here, we develop one-parameter descent extensions of the method based on the Dai–Liao approach. We show that one of the given methods satisfies the sufficient descent condition when the parameter is chosen properly. Also, we establish global convergence of the method without convexity assumption. At last, practical merits of the methods are investigated by numerical experiments on a set of CUTEr test functions as well as the signal processing problems. The results show computational efficiency of the proposed methods.

最近，Jian、Han 和 Jiang 提出了一种全局收敛的下降混合共轭梯度方法，该方法在目标函数上没有凸性假设，从计算的角度来看也很有前景。在这里，我们基于 Dai-Liao 方法开发了该方法的单参数下降扩展。我们表明，当参数选择正确时，给定的方法之一满足充分下降条件。此外，我们在没有凸性假设的情况下建立了该方法的全局收敛性。最后，通过对一组CUTEr测试函数以及信号处理问题的数值实验，研究了这些方法的实际优点。结果显示了所提出方法的计算效率。