A new relaxed CQ algorithm for solving split feasibility problems in Hilbert spaces and its applications

Inspired by the works of Lopez et al. [ 21 ] and the recent paper of Dang et al. [ 15 ], we devise a new inertial relaxation of the CQ algorithm for solving Split Feasibility Problems (SFP) in real Hilbert spaces. Under mild and standard conditions we establish weak convergence of the proposed algorithm. We also propose a Mann-type variant which converges strongly. The performances and comparisons with some existing methods are presented through numerical examples in Compressed Sensing and Sparse Binary Tomography by solving the LASSO problem.