具有充分下降性的修正型混合共轭梯度法

The modified hybrid conjugates gradient methods with sufficient descent property

基于已有的共轭梯度法思想,分别对两种混合共轭梯度法的搜索方向进行修正,使得新的修正型混合共轭梯度法在每步迭代都不依赖于任何线搜索而自行产生充分下降方向。在适当的条件下,证明了新算法在Wolfe线搜索下的全局收敛性。数值实验表明该方法是有效的。

With the existing conjugate gradient method, the search directions of two hybrid conjugate gradient methods were modified, such that the new hybrid conjugate gradient methods can automatically generate sufficient descent direc- tion independent of the line search used for each iteration. Under appropriate conditions and the Wolfe line search, it was proved that the new methods are globally convergent. Preliminary numerical results show that the methods are effi- cient.