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A modified subgradient extragradient method with non-monotonic step sizes for solving quasimonotone variational inequalities

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Abstract

In this work, we propose a self-adaptive projection method for solving variational inequalities with Lipschitz continuous and quasimonotone mapping (or Lipschitz continuous mapping without monotonicity) in real Hilbert space. Using the technique of double inertial steps into a single projection method, we give weak and strong convergence theorems of the proposed algorithm. The results obtained in this paper extend some recent results in the literature.

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Data availability statement

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Authors and Affiliations

  1. Faculty of Mathematical Economics, National Economics University, Hanoi City, Vietnam

    Duong Viet Thong, Hoang Van Thang & Luong Van Long

  2. School of Mathematics and Statistics, Shandong University of Technology, Zibo, 255000, China

    Xiao-Huan Li

  3. University of Science, Vietnam National University, Hanoi, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam

    Vu Tien Dung

Authors
  1. Duong Viet Thong
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  2. Xiao-Huan Li
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  3. Vu Tien Dung
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  4. Hoang Van Thang
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  5. Luong Van Long
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Correspondence to Vu Tien Dung.

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Thong, D.V., Li, XH., Dung, V.T. et al. A modified subgradient extragradient method with non-monotonic step sizes for solving quasimonotone variational inequalities. Comp. Appl. Math. 43, 198 (2024). https://doi.org/10.1007/s40314-024-02699-2

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  • DOI: https://doi.org/10.1007/s40314-024-02699-2

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