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<p>In this paper, based on Mann-type and Halpern-type algorithms, we introduce two modified extragradient algorithms with novel stepsize rules and inertial technique for solving pseudo-monotone variational inequality problems in Hilbert and reflexive Banach spaces. Under some reasonable assumptions on the parameters, strong convergence and R-linear convergence results for our methods are established without prior knowledge of the Lipschitz constant of the bounded operator. Moreover, we provide some numerical experiments to demonstrate the efficiency of our proposed algorithm, and numerical results reveal that our algorithm outruns other algorithms in the literature.</p>

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Modified Extragradient Methods with Inertial Technique for Solving Pseudo-Monotone Variational Inequality Problems

  • 期刊论文

  • 发表日期：

    2025年1月20日

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  • Qingqing Fu,
  • Gang Cai,
  • Prasit Cholamjiak,
  • Papatsara Inkrong

摘要

In this paper, based on Mann-type and Halpern-type algorithms, we introduce two modified extragradient algorithms with novel stepsize rules and inertial technique for solving pseudo-monotone variational inequality problems in Hilbert and reflexive Banach spaces. Under some reasonable assumptions on the parameters, strong convergence and R-linear convergence results for our methods are established without prior knowledge of the Lipschitz constant of the bounded operator. Moreover, we provide some numerical experiments to demonstrate the efficiency of our proposed algorithm, and numerical results reveal that our algorithm outruns other algorithms in the literature.