An Adaptive Three-Term Conjugate Gradient Method with Sufficient Descent Condition and Conjugacy Condition

doi:10.1007/s40305-019-00257-w

Journal of the Operations Research Society of China ›› 2021, Vol. 9 ›› Issue (2): 411-425.doi: 10.1007/s40305-019-00257-w

收稿日期:2018-03-23 修回日期:2018-12-05 出版日期:2021-06-30 发布日期:2021-06-08

An Adaptive Three-Term Conjugate Gradient Method with Sufficient Descent Condition and Conjugacy Condition

Xiao-Liang Dong^1,2, Zhi-Feng Dai³, Reza Ghanbari⁴, Xiang-Li Li⁵

1. School of Mathematics and Information, North Minzu University, Yinchuan 750030, China;
2. School of Mathematics Science, Nanjing Normal University, Nanjing 210023, China;
3. College of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114, China;
4. Department of Mathematical Science, Ferdowsi University of Mashhad, Mashhad, Iran;
5. School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, Gauangxi, China

Received:2018-03-23 Revised:2018-12-05 Online:2021-06-30 Published:2021-06-08
Contact: Xiao-Liang Dong, Zhi-Feng Dai, Reza Ghanbari, Xiang-Li Li E-mail:dongxl@stu.xidian.edu.cn;zhifengdai823@163.com;rghanbari@um.ac.ir;lixiangli@guet.edu.cn
Supported by:
This work was supported by First-Class Disciplines Foundation of Ningxia Hui Autonomous Region (No.NXYLXK2017B09),the National Natural Science Foundation of China (Nos.11601012,11861002,71771030),the Key Project of North Minzu University (No.ZDZX201804),Natural Science Foundation of Ningxia Hui Autonomous Region (Nos.NZ17103,2018AAC03253),Natural Science Foundation of Guangxi Zhuang Autonomous Region (No.2018GXNSFAA138169),Guangxi Key Laboratory of Cryptography and Information Security (No.GCIS201708).

摘要/Abstract

Abstract: In this paper, an adaptive three-term conjugate gradient method is proposed for solving unconstrained problems,which generates sufficient descent directions at each iteration. Different from the existent methods, a dynamical adjustment between Hestenes–Stiefel and Dai–Liao conjugacy conditions in our proposed method is developed. Under mild condition, we show that the proposed method converges globally. Numerical experimentation with the new method indicates that it efficiently solves the test problems and therefore is promising.

Key words: Three-term conjugate gradient method, Sufficient descent condition, Conjugacy condition, Global convergence

中图分类号:

. [J]. Journal of the Operations Research Society of China, 2021, 9(2): 411-425.

Xiao-Liang Dong, Zhi-Feng Dai, Reza Ghanbari, Xiang-Li Li. An Adaptive Three-Term Conjugate Gradient Method with Sufficient Descent Condition and Conjugacy Condition[J]. Journal of the Operations Research Society of China, 2021, 9(2): 411-425.

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An Adaptive Three-Term Conjugate Gradient Method with Sufficient Descent Condition and Conjugacy Condition

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