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<p>In this paper, we study a bilevel pseudo-monotone variational inequality problem involving non-Lipschitz operators in real Banach spaces. To solve this problem, we propose two modified Mann-type methods with double inertial extrapolation. The first and second algorithms are based on the subgradient extragradient method and Tseng’s extragradient method, respectively. The proposed methods incorporate novel adaptive step sizes and do not require any line search procedures. We prove strong convergence theorems for both methods under suitable assumptions. Furthermore, we apply the main results to a bilevel constrained convex minimization problem. Finally, we present three numerical experiments, including an image restoration problem, to demonstrate the efficiency and advantages of the proposed methods and to compare.</p>

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Strongly Convergent Mann-Type Iterations with Double Inertial Extrapolation for Bilevel Pseudo-Monotone Variational Inequalities in Banach Spaces

  • 期刊论文

  • 发表日期：

    2025年9月3日

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  • Kanikar Muangchoo,
  • Pongsakorn Sunthrayuth,
  • Woraphak Nithiarayaphaks,
  • Poom Kumam

摘要

In this paper, we study a bilevel pseudo-monotone variational inequality problem involving non-Lipschitz operators in real Banach spaces. To solve this problem, we propose two modified Mann-type methods with double inertial extrapolation. The first and second algorithms are based on the subgradient extragradient method and Tseng’s extragradient method, respectively. The proposed methods incorporate novel adaptive step sizes and do not require any line search procedures. We prove strong convergence theorems for both methods under suitable assumptions. Furthermore, we apply the main results to a bilevel constrained convex minimization problem. Finally, we present three numerical experiments, including an image restoration problem, to demonstrate the efficiency and advantages of the proposed methods and to compare.