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<p>In this work, we introduce an extragradient method with one-step inertial and self-adaptive step sizes to solve variational inequalities. We obtained weak convergence of the generated sequence under some appropriate conditions on both the iterative parameters and operator. In particular, our algorithm uses new explicit step sizes which plays an important role in improving the speed of the algorithm and weak convergence is obtained without using the monotonicity of the cost operator with one projection onto the feasible set and two evaluations of the operator per iteration. Finally, some numerical results show that our method is efficient and competitive with other methods in the literature.</p>

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An Inertial Extragradient Method for Solving Variational Inequalities Without Monotonicity

  • 期刊论文

  • 发表日期：

    2026年1月22日

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  • Duong Viet Thong,
  • Xiao-Huan Li,
  • Hoang Van Thang,
  • Luong Van Long

摘要

In this work, we introduce an extragradient method with one-step inertial and self-adaptive step sizes to solve variational inequalities. We obtained weak convergence of the generated sequence under some appropriate conditions on both the iterative parameters and operator. In particular, our algorithm uses new explicit step sizes which plays an important role in improving the speed of the algorithm and weak convergence is obtained without using the monotonicity of the cost operator with one projection onto the feasible set and two evaluations of the operator per iteration. Finally, some numerical results show that our method is efficient and competitive with other methods in the literature.