Linear Convergence of Split Equality Common Null Point Problem with Application to Optimization Problem

Abstract

The purpose of this paper is to propose an iterative algorithm for solving the split equality common null point problem (SECNP), which is to find an element of the set of common zero points for a finite family of maximal monotone operators in Hilbert spaces. We introduce the concept of bounded linear regularity for the SECNP and construct several sufficient conditions to ensure the linear convergence of the algorithm. Moreover, some numerical experiments are given to test the validity of our results.