Strong convergence method for monotone inclusion problem with alternating inertial steps

Abstract

This article proposes a strong convergence of the forward-backward splitting method for a monotone inclusion problem with alternated inertial extrapolation step in a real Hilbert space. The proposed method converges strongly under some suitable and easy to verify assumptions. The advantage of our iterative scheme is that the single-valued operator is Lipschitz continuous monotone rather than cocoercive and Lipschitz constant does not require to be known. Finally, we give some numerical experiments of the proposed algorithm to demonstrate the advantages of our algorithm over the existing related ones.