SOME NOVEL INERTIAL BALL-RELAXED CQ ALGORITHMS FOR SOLVING THE SPLIT FEASIBILITY PROBLEM WITH MULTIPLE OUTPUT SETS

The split feasibility problem with multiple output sets (SFPMOS) is a generalization of the well-known split feasibility problem (SFP), which has gained significant research attention due to its applications in theoretical and practical problems. However, the original CQ method for solving the SFP seems less efficient when the involved subsets are general convex sets since the method requires calculating projection onto the given sets directly. The relaxed CQ method was introduced to overcome this difficulty when the subsets are level sets of convex functions, where the projections onto the constructed half-spaces were used instead of the projections onto the original subsets. In this paper, we propose and investigate new algorithms for solving the SFPMOS when the involved subsets are given as the level sets of strongly convex functions. In this situation, we replace the half-spaces in the relaxed CQ method with balls constructed in each iteration. The algorithms are accelerated using the inertial technique and eliminate the need for calculating or estimating the norms of linear operators by employing self-adaptive step size criteria. We then analyze the strong convergence of the algorithms under some mild conditions. Some applications to the split feasibility problem are also reported. Finally, we present three numerical results, including an application to the LASSO problem with elastic net regularization, illustrating the better performance of our algorithms compared to the relevant ones.