In this paper, we study the strong convergence of two Mann-type inertial extragradient algorithms, which are devised with a new step size, for solving a variational inequality problem with a monotone and Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems for the suggested algorithms are proved without the prior knowledge of the Lipschitz constant of the operator. Finally, we provide some numerical experiments to illustrate the performance of the proposed algorithms and provide a comparison with related ones.

中文翻译：

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求解变分不等式问题的自适应惯性引力算法

在本文中，我们研究了两种Mann型惯性超梯度算法的强收敛性，它们用新的步长设计，用于解决实希尔伯特空间中单调和Lipschitz连续算子的变分不等式问题。在没有算子的Lipschitz常数的先验知识的情况下，证明了所建议算法的强收敛定理。最后，我们提供了一些数值实验来说明所提出算法的性能，并与相关算法进行比较。