ABSTRACT

In this paper, we propose a single projection method for finding a solution of the bilevel pseudo-monotone variational inequality problem in real Hilbert spaces. The advantage of the proposed algorithm requires only one projection onto the feasible set. Also, we prove strong convergence theorems of the proposed method under mild conditions, which improve some related results in the literature. Finally, we present some numerical experiments to show the efficiency and advantages of the proposed algorithm.

中文翻译：

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求解双层伪单调变分不等式问题的自适应步长投影收缩法

摘要

在本文中，我们提出了一种单投影方法来求解真实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只需要在可行集上进行一次投影。此外，我们证明了该方法在温和条件下的强收敛定理，从而改进了文献中的一些相关结果。最后，我们提出了一些数值实验来展示所提出算法的效率和优势。