We introduce two inertial extragradient algorithms for solving a bilevel pseudomonotone variational inequality problem in real Hilbert spaces. The advantages of the proposed algorithms are that they can work without the prior knowledge of the Lipschitz constant of the involving operator and only one projection onto the feasible set is required. Strong convergence theorems of the suggested algorithms are obtained under suitable conditions. Finally, some numerical examples are provided to show the efficiency of the proposed algorithms.

中文翻译：

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求解二级伪单调变分不等式问题的自适应惯性超梯度算法

我们介绍了两种惯性超梯度算法，用于解决实际希尔伯特空间中的双层伪单调变分不等式问题。所提出算法的优点是它们可以在不涉及参与算子的Lipschitz常数的情况下工作，并且只需要对可行集进行一次投影。在适当的条件下获得了所建议算法的强收敛定理。最后，提供了一些数值示例来说明所提出算法的效率。