A RELAXED INERTIAL METHOD FOR SOLVING THE SPLIT FEASIBILITY PROBLEM IN HILBERT SPACES

Abstract

Since its introduction in 1994, the split feasibility problem has found numerous practical applications in various fields, such as digital engineering and medicine. In this paper, we investigate and address the split feasibility problem in real Hilbert spaces. We propose a novel method that leverages the inertial technique combined with a relaxation technique with a self- adaptive step size criterion to approximate the solution of the problem. The proposed method achieves strong convergence under some conditions on the control parameters and without prior knowledge of the transformation operators and the monotone and Lipschitz continuous constants of the involved operators. Additionally, we apply our algorithm to image restoration problems, comparing the effectiveness of the new method with the methods being compared. The experimental results validate that the proposed method not only ensures feasibility but also enhances efficiency in solving image restoration problems. This confirms the wide applicability and high practicality of the method we have developed.