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More on Arago'n Artacho -- Campoy's Algorithm Operators

Salihah Thabet Alwadani

Abstract

The Arago'n Artacho--Campoy algorithm (AACA) is a new method for finding zeros of sums of monotone operators. In this paper we complete the analysis of their algorithm by defining their operator using Douglas Rachford operator and then study the effects of the order of the two possible Arago'n Artacho--Campoy operators.

More on Arago'n Artacho -- Campoy's Algorithm Operators

Abstract

The Arago'n Artacho--Campoy algorithm (AACA) is a new method for finding zeros of sums of monotone operators. In this paper we complete the analysis of their algorithm by defining their operator using Douglas Rachford operator and then study the effects of the order of the two possible Arago'n Artacho--Campoy operators.
Paper Structure (2 sections, 7 theorems, 60 equations)

This paper contains 2 sections, 7 theorems, 60 equations.

Table of Contents

  1. Introduction
  2. New Results

Key Result

Proposition 2.1

Let $\gamma \in \left] 0, 1 \right[$ and suppose that $A$ is an affine relation. Then the following hold;

Theorems & Definitions (16)

  • Proposition 2.1
  • proof
  • Lemma 2.2
  • proof
  • Example 2.3
  • proof
  • Lemma 2.4
  • proof
  • Lemma 2.5
  • proof
  • ...and 6 more