A NEW CONJUGATE GRADIENT METHOD AND ITS GLOBAL CONVERGENCE PROPERTIES

查看全文 作　　者：LI Zhengfeng CHEN Jing DENG Naiyang(Division of Basic Sciences, China Agricultural University East Campus, Beijing 100083, China) 出　　处：《Systems Science and Mathematical Sciences》索引1998年第11卷第1期,共8页 摘　　要：This paper presents a new conjugate gradient method for unconstrained opti-mization. This method reduces to the Polak-Ribiere-Polyak method when line searches areexact. But their performances are differellt in the case of inexact line search. By a simpleexample, we show that the Wolf e conditions do not ensure that the present method and thePolak- Ribiere- Polyak method will pro duce descent direct i0ns even u nder t h e ass umpt ionthat the objective function is Strictly convex. This result contradicts the F0lk axiom thatthe Polak-Ribiere-Polyak with the Wolf e line search should find the minimizer of a strictlyconvex objective function. Finally, we show that there are two ways to improve the newmethod such that it is globally convergent. 关 键 词：CONJUGATE GRADIENT method global CONVERGENCE UNCONSTRAINED optimization line searches.