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

• 论文 • 上一篇    下一篇

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. 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. 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: 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