An efficient adaptive three-term extension of the Hestenes-Stiefel conjugate gradient method

被引：2

作者：

Dong, Xiao-Liang ^{[1
,2
]}

Liu, Ze-Xian ^{[3
,4
]}

Liu, Hong-Wei ^{[4
]}

Li, Xiang-Li ^{[5
]}

机构：

[1] Nanjing Normal Univ, Sch Math Sci, Nanjing, Jiangsu, Peoples R China

[2] North Minzu Univ, Sch Math & Informat, Yinchuan, Peoples R China

[3] Hezhou Univ, Sch Math & Comp Sci, Hezhou, Peoples R China

[4] Xidian Univ, Sch Math & Stat, Xian, Shaanxi, Peoples R China

[5] Guilin Univ Elect Technol, Sch Math & Comp Sci, Guilin, Peoples R China

来源：

OPTIMIZATION METHODS & SOFTWARE | 2019年 / 34卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Unconstrained optimization; conjugate gradient method; conjugacy condition; sufficient descent condition; global convergence; numerical comparison; GLOBAL CONVERGENCE; DESCENT PROPERTY; ALGORITHM; RISK;

D O I：

10.1080/10556788.2017.1418870

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

A new three-term Hestenes-Stiefel-type conjugate gradient method is proposed in which the search direction can satisfy the sufficient descent condition as well as an adaptive conjugacy condition. It is notable that search directions of the method are dynamically adjusted between that of the Newton method and the 3HS+ method, accelerating the convergence or reducing the condition number of iteration matrix. Under mild conditions, we show that the proposed method converges globally for general objective functions. Numerical experiments indicate that the method is practically promising.

引用

页码：546 / 559

页数：14

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