一类修正LS谱共轭梯度法的全局收敛性  

Global Convergence of a Modified LS Spectral Conjugate Gradient Method

作　　者：胡鹏[1,2] 杜学武[1] 郭翠峰[3] 

机构地区：[1]重庆师范大学数学学院,重庆401331 [2]泸州高级中学,四川泸州646000 [3]西华大学数学与计算机科学学院,成都610039

出　　处：《重庆师范大学学报（自然科学版）》2012年第5期13-15,共3页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.10971241;No.11171363);重庆师范大学自然科学基金(No.08XLR022)

摘　　要：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。Spectral conjugate gradient method is a kind of method that combines conjugate gradient method with spectral gradient meth- od. In 2001, it was first put forward by Birgin and Martinez in [8], but this method can not always guarantee to generate descent di- rections. This paper first gives out a modified Liu-Storey formula which uses the modified method given by literature ~10~, 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.

关 键 词：修正的Liu-Storey共轭梯度法 ARMIJO型线搜索 全局收敛性 

分 类 号：O221.2[理学—运筹学与控制论]