Linear convergence of the relaxed gradient projection algorithm for solving the split equality problems in Hilbert spaces

Abstract

Abstract In this paper, we consider the relaxed gradient projection algorithm to solve the split equality problem in Hilbert spaces, and we investigate its linear convergence. In particular, we use the concept of the bounded linear regularity property for the split equality problem to prove the linear convergence property for the above algorithm. Furthermore, we conclude the linear convergence rate of the relaxed gradient projection algorithm. Finally, some numerical experiments are given to test the validity of our results.

Keywords

• Linear convergence
• Split equality problem
• Bounded linear regularity
• Relaxed gradient projection algorithm