一类混合HS和DY共轭梯度法及其全局收敛性

A Mixed HS and DY Conjugate Gradient Method and Its Global Convergence

为了寻找同时具有良好的收敛性和数值效果的共轭梯度法.本文将HS方法和DY方法结合,选用Wolfe线搜索,构造出了一类新的混合共轭梯度法.并在Wolfe线搜索的条件下证明了该算法全局收敛性.对新算法进行数值实验,并与HS方法和DY方法的数值结果进行了比较,结果表明新算法是有效的.

The aim is to find a conjugate gradient method with good convergence and numerical expression at the same time. In this paper,combining the HS method and the DY method,and using Wolfe line search,a new hybrid conjugate gradient method has been developed. Global convergence of new methods under Wolfe line search has been proved. The numerical experiments are performed on the new hybrid algorithm. Compared with the numerical resluts of the HS method and the DY method,the results show that the new algorithm is effective.