A dynamical system with fixed-time convergence for solving the split feasibility problem and applications to signal recovery

Abstract

In this article, we first transform the split feasibility problem into the fixed point problem and focus on a novel dynamical system to solve the fixed point problem. The existence and uniqueness of the solution of the dynamical system are revealed. Under mild conditions, we derive that the solution of the proposed method globally converges to the solution of the split feasibility problem. Furthermore, the convergence time of the dynamical system can be upper bounded which is independent of any initial state. Finally, numerical experiments on signal processing and image restoration are presented to demonstrate the efficiency and competitiveness of the proposed method.