The objective of this article is to solve pseudomonotone variational inequality problems in a real Hilbert space. We introduce an inertial algorithm with a new self-adaptive step size rule, which is based on the projection and contraction method. Only one step projection is used to design the proposed algorithm, and the strong convergence of the iterative sequence is obtained under some appropriate conditions. The main advantage of the algorithm is that the proof of convergence of the algorithm is implemented without the prior knowledge of the Lipschitz constant of cost operator. Numerical experiments are also put forward to support the analysis of the theorem and provide comparisons with related algorithms.

中文翻译：

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求解伪单调变分不等式问题的改进惯性投影和收缩方法

本文的目的是解决真实希尔伯特空间中的赝单调变分不等式问题。我们引入了一种具有新的自适应步长规则的惯性算法，该算法基于投影和收缩方法。该算法仅采用一步投影进行设计，在一定条件下得到迭代序列的强收敛性。该算法的主要优点是算法收敛的证明是在没有成本算子的Lipschitz常数的先验知识的情况下实现的。还提出了数值实验来支持定理的分析并提供与相关算法的比较。