A Modified Hestenes-Stiefel Conjugate Gradient Method and Its Convergence

作     者：Zeng Xin WEI Hai Dong HUANG Yah Rong TAO 

作者机构：College of Mathematics and Information Science Guangxi University Guangxi 530004 P. R. China 

出 版 物：《Journal of Mathematical Research and Exposition》 (数学研究与评论（英文版）)

年 卷 期：2010年第30卷第2期

页      面：297-308页

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 081401[工学-岩土工程] 08[工学] 070105[理学-运筹学与控制论] 0814[工学-土木工程] 0701[理学-数学] 

基　　金：Supported by the National Natural Science Foundation of China (Grant No.10761001) 

主　　题：conjugate gradient method sufficient descent condition line search global convergence. 

摘      要：It is well-known that the direction generated by Hestenes-Stiefel （HS） conjugate gradient method may not be a descent direction for the objective function. In this paper, we take a little modification to the HS method, then the generated direction always satisfies the sufficient descent condition. An advantage of the modified Hestenes-Stiefel （MHS） method is that the scalar βκHS. keeps nonnegative under the weak Wolfe-Powell line search. The global convergence result of the MHS method is established under some mild conditions. Preliminary numerical results show that the MHS method is a little more efficient than PRP and HS methods.