For solving pseudo-monotone variational inequality problems in Hilbert spaces, we introduce a new algorithm with self-adaptive technique. The algorithm is based on the projection method and inertial method. The strong convergence theorem is established under some appropriate conditions. Finally, we provide some numerical experiments to illustrate the effectiveness and advantages of the proposed algorithm.

中文翻译：

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求解希尔伯特空间伪单调变分不等式问题的自适应惯性修正投影算法

为了解决希尔伯特空间中的伪单调变分不等式问题，我们引入了一种具有自适应技术的新算法。该算法基于投影法和惯性法。强收敛定理是在某些适当的条件下成立的。最后，我们提供了一些数值实验来说明所提出算法的有效性和优势。