A Primal-dual Backward Reflected Forward Splitting Algorithm for Structured Monotone Inclusions

We propose a primal-dual backward reflected forward splitting method for solving structured primal-dual monotone inclusions in real Hilbert spaces. The algorithm allows to use the inexact computations of Lipschitzian and cocoercive operators. The strong convergence of the generated iterative sequence is proved under the strong monotonicity condition, whilst the weak convergence is formally proved under several conditions used in the literature. An application to a structured minimization problem is provided.