A new method for solving split equality problems via projection dynamical systems

Abstract

In this paper, we propose a projection dynamical system for solving the split equality problem, or more generally the approximate split equality problem, in Hilbert spaces. The proposed dynamical system endows with the continuous behavior with time for Moudafi’s alternating CQ-algorithm and Byrne and Moudafi’s extended CQ-algorithm. Under mild conditions, we prove that the trajectory of the dynamical system converges weakly to a solution of the approximate split equality problem as time variable t goes to $+\infty $. We further derive the exponential-type convergence provided that a bounded linear regularity property holds for the approximate split equality problem. Several numerical examples are given to demonstrate the validity and transient behavior of the proposed method.