一类修正LS谱共轭梯度法的全局收敛性 (运筹学与控制论)

谱共轭梯度法是一类将共轭梯度法和谱梯度法相结合的方法。2001年由Birgin和Martinez首先提出,但该方法不能保证始终产生下降方向。本文用已有的修正方法,给出一个修正的Liu-Storey公式,并结合谱梯度法,提出了一个具有充分下降性的修正Liu-Storey谱共轭梯度法,证明了该方法在标准Armijo非精确线搜索下的全局收敛性,并易推知该方法在Armijo-Goldstein非精确线搜索准则下同样满足全局收敛性。给出的数值实验表明,新算法略优于LS方法。

Global Convergence of a Modified LS Spectral Conjugate Gradient Method

Spectral conjugate gradient method is a kind of method that combines conjugate gradient method with spectral gradient method.In 2001,it was first put forward by Birgin and Martinez in 8],but this method can not always guarantee to generate descent directions.This paper first gives out a modified Liu-Storey formula which uses the modified method given by literature ,and then combines the modified Liu-Storey formula with the spectral gradient method,putting forward a modified Liu-Storey spectral conjugate gradient method satisfying the sufficient descent condition.And the global convergence of the method with the standard Armijo inexact line search is proved;it is easy to deduce the method also satisfying the global convergence under the Armijo-Goldstein inexact line search rule.The given numerical results show that the new method is a little better than LS method.