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Linear convergence of an iterative algorithm for solving the multiple-sets split equality problem

In this paper, we propose a subgradient projection algorithm for solving the multiple-sets split equality problem (MSSEP), and investigate its linear convergence. We involve the bounded linear regularity for the MSSEP, and construct several sufficient conditions to ensure the linear convergence of our proposed algorithm. One of the highlights of our algorithm is that metric projections onto given feasibility sets are easily calculated (that is, the projections onto half-spaces). Some numerical results are provided to illustrate the validity of our proposed algorithm.