A Novel Algorithm and Its Convergence Analysis for Solving the Generalized Split Inverse Problem

Abstract

In this paper, we consider a bilevel problem: Variational inequalities over the solution set of a general split inverse problem consists of a monotone variational inclusion problem. We propose a relaxed inertial forward-backward-forward splitting algorithm with a new step size rule for finding an approximate solution of this problem in real Hilbert spaces. Under some mild conditions, we prove a strong convergence theorem for the algorithm produced by the method. Also, we apply our result to study certain classes of bilevel optimization problems, and split inverse problems. Finally, we present some numerical experiments and application in signal recovery problem to demonstrate the efficiency of the proposed algorithm.