DOUBLE INERTIAL PARAMETERS FORWARD-BACKWARD SPLITTING METHOD: APPLICATIONS TO COMPRESSED SENSING, IMAGE PROCESSING, AND SCAD PENALTY PROBLEMS

In this paper, a forward-backward splitting algorithm with two inertial parameters (one non-negative and the other non-positive) extrapolation step is proposed for finding a zero point of the sum of maximal monotone and co-coercive operators in real Hilbert spaces. One of the interesting features of our proposed algorithm is that no online rule on the inertial parameters with the iterates is needed. The weak convergence result of the proposed algorithm is established under some standard assumptions. Numerical results arising from LASSO problems in compressed sensing, image processing, and SCAD penalty problems are provided to illustrate the behavior of our proposed algorithm.