The purpose of this paper is to investigate a new inertial self-adaptive iterative algorithm for solving variational inequalities over the solution set of the split variational inequality problem with multiple output sets in real Hilbert spaces. The strong convergence result is given under some mild conditions widely used in the convergence analysis. Our algorithm is accelerated by the inertial technique and eliminates the dependence on the norm of the transformation operators and the strongly monotone and Lipschitz continuous constants of the involved operator. Two applications in the network bandwidth allocation problem and the image classification problem are shown, and some numerical experiments are presented to show the advantages of the proposed algorithm.

本文的目的是研究一种新的惯性自适应迭代算法，用于求解实希尔伯特空间中具有多个输出集的分裂变分不等式问题的解集上的变分不等式。在收敛分析中广泛使用的一些温和条件下给出了强收敛结果。我们的算法通过惯性技术加速，消除了对变换算子范数以及所涉及算子的强单调和Lipschitz连续常数的依赖。展示了网络带宽分配问题和图像分类问题中的两个应用，并进行了一些数值实验以展示所提出算法的优点。