Outer perturbations of a projection method and two approximation methods for the split equality problem

Abstract

In this article, we first present a projection method with outer perturbations for the split equality problem (SEP) and establish its weak convergence. Then combining the proposed projection method with the outer approximation method and Halpern iteration method, we introduce two approximation methods to solve the SEP, where the two closed convex sets are both level sets of convex functions. Finally, a preliminary experiment presented compares the approximation methods and a relaxed projection method.