Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (2): 795-812.doi: 10.1007/s10473-022-0224-7

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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.

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

CLC Number: 

  • 65Y05
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