A reflected forward-backward splitting method for monotone inclusions involving Lipschitzian operators

Understand

The proximal extrapolated gradient method \cite{Malitsky18a} is an extension of the projected reflected gradient method \cite{Malitsky15}.

• Both methods were proposed for solving the classic variational inequalities.
• In this paper, we investigate the projected reflected gradient method, in the general setting, for solving monotone inclusions involving Lipschitzian operators.
• As a result, we obtain a simple method for finding a zero point of the sum of two monotone operators where one of them is Lipschizian.