The main purpose of this paper is to propose a new modified contraction method for solving a certain class of split monotone variational inclusion problems in real Hilbert spaces. We prove that the sequence generated by the proposed method converges strongly to a solution of the aforementioned problem. Our strong convergence result is obtained when the underline operator is monotone and Lipschitz continuous, and the knowledge of its Lipschitz constant is not required. As application, we solved the split linear inverse problems, for which we also considered a special case of this problem, namely, the LASSO problem. We also give some numerical illustrations of the proposed method in comparison with other methods in the literature to further show the applicability and advantage of our results. The results obtained in this paper generalize and improve many recent results in this direction.

本文的主要目的是提出一种新的改进的压缩方法，用于解决实际希尔伯特空间中的一类分裂单调变分包含问题。我们证明了由所提出的方法产生的序列强烈收敛于上述问题的解决方案。当下划线算子为单调且Lipschitz连续时，不需要对Lipschitz常数的知识，便获得了较强的收敛结果。作为应用，我们解决了分裂线性逆问题，为此我们还考虑了该问题的特例，即LASSO问题。与文献中的其他方法相比，我们还给出了所提出方法的一些数值说明，以进一步证明我们的结果的适用性和优势。