Convergence rate of the relaxed CQ algorithm under Hölderian type error bound property

Abstract

The relaxed CQ algorithm is one of the most important algorithms for solving the split feasibility problem. We study the issue of strong convergence of the relaxed CQ algorithm in Hilbert spaces together with estimates on the convergence rate. Under a kind of Hölderian type bounded error bound property, strong convergence of the relaxed CQ algorithm is established. Furthermore, qualitative estimates on the convergence rate is presented. In particular, for the case when the involved exponent is equal to 1, the linear convergence of the relaxed CQ algorithm is established. Finally, numerical experiments are performed to show the convergence property of the relaxed CQ algorithm for the compressed sensing problem.