A Novel Relaxed Method for the Split Feasibility Problem in Hilbert Spaces

In this paper, we propose a novel relaxed method in order to solve the split feasibility problem in Hilbert spaces. Our algorithms involve a new strategy where the projection onto the half-space is replaced by the projection onto the intersection of two half-spaces. In addition, our algorithms do not require any prior information about the operator norm. We also establish the weak convergence and strong convergence of the proposed algorithms under standard conditions. Finally, the results of numerical experiments indicate that the proposed algorithm is effective in the LASSO problem.