A novel inertial proximal contraction-type algorithm with self-adaptive step size for solving monotone variational inclusion problems

In this paper, we present a novel accelerated proximal contraction-type algorithm for solving monotone variational inclusion problems in real Hilbert spaces. Our method introduces a self-adaptive step-size technique, eliminating the need for a priori knowledge of the operator norm. Additionally, we employ a two-step inertial method with a correction term to enhance convergence speed. We establish the strong convergence of the proposed algorithms under suitable conditions imposed on parameters. Furthermore, we apply our results to study a convex minimization problem. Finally, we provide theoretical and practical applications in signal processing to demonstrate and evaluate the performance of our method compared to related methods in the literature.