STRONG CONVERGENCE OF AN INERTIAL EXTRAGRADIENT METHOD WITH AN ADAPTIVE NONDECREASING STEP SIZE FOR SOLVING VARIATIONAL INEQUALITIES

doi:10.1007/s10473-022-0224-7

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (2): 795-812.doi: 10.1007/s10473-022-0224-7

STRONG CONVERGENCE OF AN INERTIAL EXTRAGRADIENT METHOD WITH AN ADAPTIVE NONDECREASING STEP SIZE FOR SOLVING VARIATIONAL INEQUALITIES

Nguyen Xuan LINH¹, Duong Viet THONG², Prasit CHOLAMJIAK³, Pham Anh TUAN⁴, Luong Van LONG⁴

1. Department of Mathematics Mathematics, Falcuty of Information Technology, National University of Civil Engineering;
2. Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, Vietnam;
3. School of Science, University of Phayao, Phayao 56000, Thailand;
4. Faculty of Mathematical Economics, National Economics University, Hanoi City, Vietnam

收稿日期:2020-12-18 修回日期:2021-03-19 出版日期:2022-04-25 发布日期:2022-04-22
通讯作者: Duong Viet THONG,E-mail:duongvietthong@tdmu.edu.vn E-mail:duongvietthong@tdmu.edu.vn
作者简介:Nguyen Xuan LINH,E-mail:linhnx@nuce.edu.vn;Prasit CHOLAMJIAK,E-mail:prasitch2008@yahoo.com;Pham Anh TUAN,E-mail:patuan.1963@gmail.com;Luong Van LONG,E-mail:longtkt@gmail.com
基金资助:
This research is funded by National University of Civil Engineering (NUCE) under grant number 15-2020/KHXD-TD.

STRONG CONVERGENCE OF AN INERTIAL EXTRAGRADIENT METHOD WITH AN ADAPTIVE NONDECREASING STEP SIZE FOR SOLVING VARIATIONAL INEQUALITIES

Nguyen Xuan LINH¹, Duong Viet THONG², Prasit CHOLAMJIAK³, Pham Anh TUAN⁴, Luong Van LONG⁴

1. Department of Mathematics Mathematics, Falcuty of Information Technology, National University of Civil Engineering;
2. Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, Vietnam;
3. School of Science, University of Phayao, Phayao 56000, Thailand;
4. Faculty of Mathematical Economics, National Economics University, Hanoi City, Vietnam

Received:2020-12-18 Revised:2021-03-19 Online:2022-04-25 Published:2022-04-22
Supported by:
This research is funded by National University of Civil Engineering (NUCE) under grant number 15-2020/KHXD-TD.

摘要/Abstract

摘要： In this work, we investigate a classical pseudomonotone and Lipschitz continuous variational inequality in the setting of Hilbert space, and present a projection-type approximation method for solving this problem. Our method requires only to compute one projection onto the feasible set per iteration and without any linesearch procedure or additional projections as well as does not need to the prior knowledge of the Lipschitz constant and the sequentially weakly continuity of the variational inequality mapping. A strong convergence is established for the proposed method to a solution of a variational inequality problem under certain mild assumptions. Finally, we give some numerical experiments illustrating the performance of the proposed method for variational inequality problems.

关键词: Inertial method, Tseng's extragradient, viscosity method, variational inequality problem, pseudomonotone mapping, strong convergence

Abstract: In this work, we investigate a classical pseudomonotone and Lipschitz continuous variational inequality in the setting of Hilbert space, and present a projection-type approximation method for solving this problem. Our method requires only to compute one projection onto the feasible set per iteration and without any linesearch procedure or additional projections as well as does not need to the prior knowledge of the Lipschitz constant and the sequentially weakly continuity of the variational inequality mapping. A strong convergence is established for the proposed method to a solution of a variational inequality problem under certain mild assumptions. Finally, we give some numerical experiments illustrating the performance of the proposed method for variational inequality problems.

Key words: Inertial method, Tseng's extragradient, viscosity method, variational inequality problem, pseudomonotone mapping, strong convergence

中图分类号:

65Y05

Nguyen Xuan LINH, Duong Viet THONG, Prasit CHOLAMJIAK, Pham Anh TUAN, Luong Van LONG. STRONG CONVERGENCE OF AN INERTIAL EXTRAGRADIENT METHOD WITH AN ADAPTIVE NONDECREASING STEP SIZE FOR SOLVING VARIATIONAL INEQUALITIES[J]. 数学物理学报(英文版), 2022, 42(2): 795-812.

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STRONG CONVERGENCE OF AN INERTIAL EXTRAGRADIENT METHOD WITH AN ADAPTIVE NONDECREASING STEP SIZE FOR SOLVING VARIATIONAL INEQUALITIES

STRONG CONVERGENCE OF AN INERTIAL EXTRAGRADIENT METHOD WITH AN ADAPTIVE NONDECREASING STEP SIZE FOR SOLVING VARIATIONAL INEQUALITIES

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