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

Vu Cong Bang, Dimitri Papadimitriou, Vu Xuan Nham

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.

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

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.
Paper Structure (4 sections, 8 theorems, 70 equations, 1 algorithm)

This paper contains 4 sections, 8 theorems, 70 equations, 1 algorithm.

Table of Contents

  1. Introduction
  2. Notation and Background
  3. Main results
  4. Application to structured minimization problems

Key Result

Lemma 2.4

plc6 Suppose that the condition c:1 is satisfied. Then, $\operatorname{zer}(\boldsymbol{A}+\boldsymbol{S}+\boldsymbol{B})\not={\varnothing}$. Furthermore,

Theorems & Definitions (17)

  • Definition 2.1
  • Definition 2.2
  • Lemma 2.4
  • Lemma 2.5
  • Lemma 2.6
  • Theorem 3.3
  • proof
  • Theorem 3.4
  • proof
  • Corollary 3.5
  • ...and 7 more