一类混合共轭梯度算法

A Class Hybrid Conjugate Gradient Methods

改进了戴志锋,陈兰平提出的HS-DY混合共轭梯度法,扩大了参数kβ的取值范围,基于同样的考虑,给出了DY与PRP算法相结合的混合共轭梯度法,在Wolfe线搜索下不需给定下降条件即证明了它们的全局收敛性.数值实验表明这类的算法十分有效.

In this paper, we improve the hybrid of conjugate gradient method for unconstrained optimization based on Hestenesstiefel Algorithms and Dai-Yuan Algorithms. This paper allows βk to be selected in a wider than Dai-Yuan Algorithms. Based the same thinking, we propose a mixed conjugate gradient method for unconstrained optimization based on Polak- Ribiere-Polyak Algorithms and Dai-Yuan Algorithms, which has taken the advantages of two Algorithms. We proved they can ensure the convergence of the new methods under the Wolfe line search and withouth the descent condition. Numerical experiments show that the algoriths are efficient by comparing with HS conjugate gradient method and PR conjugate gradient method.