A SELF-ADAPTIVE ITERATIVE METHOD FOR APPROXIMATING THE SOLUTION OF 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 propose a new iterative method for approximating the solution of the split feasibility problem in real Hilbert spaces. This is achieved by solving a class of variational inequality problems over the solution set of the split feasibility problem. Our algorithm uses inertia techniques to enhance its convergence speed and applies a self-adaptive step size criterion to remove the need to know the norm of transformation operators. By incorporating convex combinations into the algorithm, our method ensures the strong convergence of the generated iterative sequence. This result is proven using mathematical lemmas and theorems under suitable assumptions imposed on the parameters. Finally, a numerical experiment in infinite-dimensional spaces is given to illustrate the effectiveness of our method and compare it with the related ones.