本文在共轭梯度不能精确计算的情况下,采用Wolfe或Armijo步长规则研究了带误差项的Dai—Yuan(abbr.DY)共轭梯度法,我们的方法的一个很重要的特征就是步长不一定趋于零。这种特征使得我们的分析对许多实际问题很有用。我们在很一般的假设条件下证明了算法的全局收敛性。最后给出了数值算例。
We consider a kind of Dai-Yuan (Abbr.DY) conjugate gradient method with Wolfe or Armijo stepsize rules in the case where the conjugate gradient is computed inexactly. An important novel feature in our theoretical analysis is that the stepsizes do not tend to zero in the limit necessarily. This feature makes our analysis applicable to various difficult problems encountered in practice. We prove the global convergence of the method under mild conditions. At the end of this paper, we give the numerical results.