New Inertial Relaxed CQ Algorithms for Solving Split Feasibility Problems in Hilbert Spaces

The split feasibility problem has received much attention due to its various applications in signal processing and image reconstruction. In this paper, we propose two inertial relaxed algorithms for solving the split feasibility problem in real Hilbert spaces according to the previous experience of applying inertial technology to the algorithm. These algorithms involve metric projections onto half-spaces, and we construct new variable step size, which has an exact form and does not need to know a prior information norm of bounded linear operators. Furthermore, we also establish weak and strong convergence of the proposed algorithms under certain mild conditions and present a numerical experiment to illustrate the performance of the proposed algorithms.