Bounded Perturbation Resilience of Two Modified Relaxed CQ Algorithms for the Multiple-Sets Split Feasibility Problem

Abstract

In this paper, we present some modified relaxed CQ algorithms with different kinds of step size and perturbation to solve the Multiple-sets Split Feasibility Problem (MSSFP). Under mild assumptions, we establish weak convergence and prove the bounded perturbation resilience of the proposed algorithms in Hilbert spaces. Treating appropriate inertial terms as bounded perturbations, we construct the inertial acceleration versions of the corresponding algorithms. Finally, for the LASSO problem and three experimental examples, numerical computations are given to demonstrate the efficiency of the proposed algorithms and the validity of the inertial perturbation.