CONVERGENCE ANALYSIS ON A CLASS OF CONJUGATE GRADIENT METHODS WITHOUT SUFFICIENT DECREASE CONDITION

数学物理学报(英文版) ›› 1998, Vol. 18 ›› Issue (1): 11-16.

CONVERGENCE ANALYSIS ON A CLASS OF CONJUGATE GRADIENT METHODS WITHOUT SUFFICIENT DECREASE CONDITION

刘光辉¹, 韩继业¹, 戚厚铎¹, 徐中玲²

1. Institute of Applied Mathematics, Academia Sinica, Beijing 100080, China;
2. Committee of National Natural Science Foundation of China. Beijing 100045. China

收稿日期:1995-03-10 修回日期:1996-06-07 出版日期:1998-03-25 发布日期:1998-03-25
基金资助:
This work is supported by the National Natural Science Foundation

CONVERGENCE ANALYSIS ON A CLASS OF CONJUGATE GRADIENT METHODS WITHOUT SUFFICIENT DECREASE CONDITION

Liu Gnanghui¹, Han Jiye¹, Qi Honduo¹, Xu Zhongling²

1. Institute of Applied Mathematics, Academia Sinica, Beijing 100080, China;
2. Committee of National Natural Science Foundation of China. Beijing 100045. China

Received:1995-03-10 Revised:1996-06-07 Online:1998-03-25 Published:1998-03-25
Supported by:
This work is supported by the National Natural Science Foundation

摘要/Abstract

摘要： Recently, Gilbert and Nocedal^[3] investigated global convergence of conjugate gradient methods related to Polak-Ribiere formular, they restricted β_K to non-negative value.[5] discussed the same problem as that in[3] and relaxed oh to be negative with the objective function being convex. This paper allows β_K to be selected in a wider range than[5]. Especially, the global convergence of the corresponding algorithm without sufficient decrease condition is proved.

关键词: Polak-Ribière conjugate gradient method, strong Wolfe line search, global convergence

Abstract: Recently, Gilbert and Nocedal^[3] investigated global convergence of conjugate gradient methods related to Polak-Ribiere formular, they restricted β_K to non-negative value.[5] discussed the same problem as that in[3] and relaxed oh to be negative with the objective function being convex. This paper allows β_K to be selected in a wider range than[5]. Especially, the global convergence of the corresponding algorithm without sufficient decrease condition is proved.

Key words: Polak-Ribière conjugate gradient method, strong Wolfe line search, global convergence

刘光辉, 韩继业, 戚厚铎, 徐中玲. CONVERGENCE ANALYSIS ON A CLASS OF CONJUGATE GRADIENT METHODS WITHOUT SUFFICIENT DECREASE CONDITION[J]. 数学物理学报(英文版), 1998, 18(1): 11-16.

Liu Gnanghui, Han Jiye, Qi Honduo, Xu Zhongling. CONVERGENCE ANALYSIS ON A CLASS OF CONJUGATE GRADIENT METHODS WITHOUT SUFFICIENT DECREASE CONDITION[J]. Acta mathematica scientia,Series B, 1998, 18(1): 11-16.

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CONVERGENCE ANALYSIS ON A CLASS OF CONJUGATE GRADIENT METHODS WITHOUT SUFFICIENT DECREASE CONDITION

CONVERGENCE ANALYSIS ON A CLASS OF CONJUGATE GRADIENT METHODS WITHOUT SUFFICIENT DECREASE CONDITION

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