A Globally Convergent Polak-Ribiere-Polyak Conjugate Gradient Method with Armijo-Type Line Search

查看全文 作　　者：Gaohang [1]Yu;Lutai [1]Guan;Zengxin [2]Wei

机构地区：[1]Department of Scientific Computation and Computer Applications, Sun Yat-Sen University, Guangzhou 510275, China;[2]College of Mathematics and Information Science, Guangxi University, Nanning530004, China

出　　处：《Numerical Mathematics A Journal of Chinese Universities(English Series)》索引2006年第15卷第4期,共10页

基　　金：This work is supported by the Chinese NSF grants 60475042 Guangxi NSF grants 0542043the Foundation of Advanced Research Center of Zhongshan University and Hong Kong 摘　　要：In this paper, we propose a globally convergent Polak-Ribiere-Polyak (PRP) conjugate gradient method for nonconvex minimization of differentiable functions by employing an Armijo-type line search which is simpler and less demanding than those defined in [4,10]. A favorite property of this method is that we can choose the initial stepsize as the one-dimensional minimizer of a quadratic modelΦ(t):= f(xk)+tgkTdk+(1/2) t2dkTQkdk, where Qk is a positive definite matrix that carries some second order information of the objective function f. So, this line search may make the stepsize tk more easily accepted. Preliminary numerical results show that this method is efficient. 关键词：非约束最优化共轭梯度法整体收敛可微函数

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A Globally Convergent Polak-Ribiere-Polyak Conjugate Gradient Method with Armijo-Type Line Search

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