ALGORITHMIC SCHEMES FOR THE MULTIPLE-SETS SPLIT EQUALITY PROBLEM

Abstract

In this paper, for solving the multiple-sets split equality problem (MSSEP), we give a general approach to construct iterative methods. We present an weakly convergent string-averaging algorithmic scheme and its relaxed variant, that contain the cyclic and simultaneous iterative methods as particular cases. Then, we also propose a combination of the steepest-descent method with one of these scheme to obtain strong convergence. In our methods, we do not need to have any information
on the operator norms. We also give numerical examples for illustrating our main methods.