A primal-dual backward reflected forward splitting algorithm for structured monotone inclusions

TL;DR

This paper introduces a primal-dual backward reflected forward splitting algorithm for structured monotone inclusions, allowing inexact computations and proving convergence under various conditions, with applications to minimization problems.

Contribution

It presents a novel primal-dual splitting method that handles inexact operator computations and establishes convergence results under strong and weak conditions.

Findings

Algorithm converges strongly under strong monotonicity.

Weak convergence is proved under standard conditions.

Applicable to structured minimization problems.

Abstract

We propose a primal-dual backward reflected forward splitting method for solving structured primal-dual monotone inclusion in real Hilbert space. The algorithm allows to use the inexact computations of the 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 conditioned used in the literature. An application to a structured minimization problem is supported.