一类具有充分下降性的混合型谱共轭梯度法

首先基于共轭梯度法的下降性条件,提出了一类结合了FR法、WYL法、PRP法优点的充分下降的混合型谱共轭梯度法.在Wolfe线搜索下用反证法证明了新的混合型谱共轭梯度法的全局收敛性.最后通过数值算例,将本文算法与WYL法、FR法进行比较,结果表明新算法在迭代次数与迭代总时间上均优于其他另外两种算法.算法的全局收敛性和数值效果的优越性表明新算法是有效的.

A Mixed Spectral Conjugate Gradient Method with Sufficient Descent Property

First, a mixed sufficiently descent spectral conjugate gradient method is put forward, which satisfies the descent condition. Besides, the method possesses the advantages of FR, WYL and PPR. Then, the global convergence of the new hybrid spectral conjugate gradient method is proved with the reduction to absurdity under the Wolfe line search. Finally, the new algorithm and the existing WYL and FR algorithms are compared in their iterative times and computing time. The comparison results show that the new algorithm is superior to the other two algorithms. The global convergence and the numerical superiority of the new algorithm indicate that it is an effective algorithm which is worth studying.