STRONGLY CONVERGENT INERTIAL FORWARD-BACKWARD-FORWARD ALGORITHM WITHOUT ON-LINE RULE FOR VARIATIONAL INEQUALITIES

doi:10.1007/s10473-024-0210-3

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (2): 551-566.doi: 10.1007/s10473-024-0210-3

STRONGLY CONVERGENT INERTIAL FORWARD-BACKWARD-FORWARD ALGORITHM WITHOUT ON-LINE RULE FOR VARIATIONAL INEQUALITIES

Yonghong YAO¹, Abubakar ADAMU², Yekini SHEHU^3,*

1. School of Mathematical Sciences, Tiangong University, Tianjin 300387, China; Center for Advanced Information Technology, Kyung Hee University, Seoul 02447, South Korea;
2. Operational Research Center in Healthcare, Near East University, TRNC Mersion 10, Nicosia 99138, Turkey; Charles Chidume Mathematics Institute, African University of Science and Technology, Abuja 900107, Nigeria;
3. School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China

收稿日期:2022-11-20 修回日期:2023-01-08 出版日期:2024-04-25 发布日期:2024-04-16
通讯作者: *Yekini SHEHU, E-mail: yekini.shehu@zjnu.edu.cn
作者简介:Yonghong YAO, E-mail: yyhtgu@hotmail.com; Abubakar ADAMU, E-mail: abubakar.adamu@neu.edu.tr

STRONGLY CONVERGENT INERTIAL FORWARD-BACKWARD-FORWARD ALGORITHM WITHOUT ON-LINE RULE FOR VARIATIONAL INEQUALITIES

Yonghong YAO¹, Abubakar ADAMU², Yekini SHEHU^3,*

1. School of Mathematical Sciences, Tiangong University, Tianjin 300387, China; Center for Advanced Information Technology, Kyung Hee University, Seoul 02447, South Korea;
2. Operational Research Center in Healthcare, Near East University, TRNC Mersion 10, Nicosia 99138, Turkey; Charles Chidume Mathematics Institute, African University of Science and Technology, Abuja 900107, Nigeria;
3. School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China

Received:2022-11-20 Revised:2023-01-08 Online:2024-04-25 Published:2024-04-16
Contact: *Yekini SHEHU, E-mail: yekini.shehu@zjnu.edu.cn
About author:Yonghong YAO, E-mail: yyhtgu@hotmail.com; Abubakar ADAMU, E-mail: abubakar.adamu@neu.edu.tr

摘要/Abstract

摘要： This paper studies a strongly convergent inertial forward-backward-forward algorithm for the variational inequality problem in Hilbert spaces. In our convergence analysis, we do not assume the on-line rule of the inertial parameters and the iterates, which have been assumed by several authors whenever a strongly convergent algorithm with an inertial extrapolation step is proposed for a variational inequality problem. Consequently, our proof arguments are different from what is obtainable in the relevant literature. Finally, we give numerical tests to confirm the theoretical analysis and show that our proposed algorithm is superior to related ones in the literature.

关键词: forward-backward-forward algorithm, inertial extrapolation, variational inequality, on-line rule

Abstract: This paper studies a strongly convergent inertial forward-backward-forward algorithm for the variational inequality problem in Hilbert spaces. In our convergence analysis, we do not assume the on-line rule of the inertial parameters and the iterates, which have been assumed by several authors whenever a strongly convergent algorithm with an inertial extrapolation step is proposed for a variational inequality problem. Consequently, our proof arguments are different from what is obtainable in the relevant literature. Finally, we give numerical tests to confirm the theoretical analysis and show that our proposed algorithm is superior to related ones in the literature.

Key words: forward-backward-forward algorithm, inertial extrapolation, variational inequality, on-line rule

中图分类号:

90C30

Yonghong YAO, Abubakar ADAMU, Yekini SHEHU. STRONGLY CONVERGENT INERTIAL FORWARD-BACKWARD-FORWARD ALGORITHM WITHOUT ON-LINE RULE FOR VARIATIONAL INEQUALITIES[J]. 数学物理学报(英文版), 2024, 44(2): 551-566.

Yonghong YAO, Abubakar ADAMU, Yekini SHEHU. STRONGLY CONVERGENT INERTIAL FORWARD-BACKWARD-FORWARD ALGORITHM WITHOUT ON-LINE RULE FOR VARIATIONAL INEQUALITIES[J]. Acta mathematica scientia,Series B, 2024, 44(2): 551-566.

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STRONGLY CONVERGENT INERTIAL FORWARD-BACKWARD-FORWARD ALGORITHM WITHOUT ON-LINE RULE FOR VARIATIONAL INEQUALITIES

STRONGLY CONVERGENT INERTIAL FORWARD-BACKWARD-FORWARD ALGORITHM WITHOUT ON-LINE RULE FOR VARIATIONAL INEQUALITIES

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