New self-adaptive step size algorithms for solving split variational inclusion problems and its applications

Abstract

In this paper, we study a special instance of the split inverse problem (SIP), which is the split variational inclusion problem (SVIP). Three simple iterative methods for solving it are introduced and weak and strong convergence theorems are established under mild and standard assumptions. As an application, the problem of minimizing two proper, convex, and lower semi-continuous functions is considered. We compare and illustrate the efficiency and applicability of our schemes for several numerical experiments as well as an example in the field of compressed sensing.