On the convergence of CQ algorithm with variable steps for the split equality problem

Abstract

We investigate CQ algorithm for the split equality problem in Hilbert spaces. In such an algorithm, the selection of the step requires prior information on the matrix norms, which is not always possible in practice. In this paper, we propose a new way to select the step so that the implementation of the algorithm does not need any prior information of the matrix norms. In Hilbert spaces, we establish the weak convergence of the proposed method to a solution of the problem under weaker conditions than usual. Preliminary numerical experiments show that the efficiency of the proposed algorithm when it applies the variable step-size.