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Self-adaptive-type CQ algorithms for split equality problems

Songxiao Li, Bing Tan, Zheng Zhou

TL;DR

Two types of algorithms and a new self-adaptive stepsize without prior knowledge of operator norms are introduced and the corresponding strong convergence theorems are obtained under mild conditions.

Abstract

The purpose of this paper is concerned with the approximate solution of split equality problems. We introduce two types of algorithms and a new self-adaptive stepsize without prior knowledge of operator norms. The corresponding strong convergence theorems are obtained under mild conditions. Finally, some numerical experiments demonstrate the efficiency of our results and compare them with the existing results.

Self-adaptive-type CQ algorithms for split equality problems

TL;DR

Two types of algorithms and a new self-adaptive stepsize without prior knowledge of operator norms are introduced and the corresponding strong convergence theorems are obtained under mild conditions.

Abstract

The purpose of this paper is concerned with the approximate solution of split equality problems. We introduce two types of algorithms and a new self-adaptive stepsize without prior knowledge of operator norms. The corresponding strong convergence theorems are obtained under mild conditions. Finally, some numerical experiments demonstrate the efficiency of our results and compare them with the existing results.

Paper Structure

This paper contains 9 sections, 9 theorems, 73 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Halpern-type CQ algorithms
  4. Self-adaptive Halpern-type CQ algorithm (SHCQA)
  5. Self-adaptive relaxed Halpern-type CQ algorithm (SRHCQA)
  6. Viscosity-type CQ algorithms
  7. Self-adaptive viscosity-type CQ algorithm (SVCQA)
  8. Self-adaptive relaxed viscosity-type CQ algorithm (SRVCQA)
  9. Numerical experiments

Key Result

lemma thmcounterlemma

Let the solution set of the split equality problem sep is nonempty. For any $\gamma>0$, a solution of SEP is equivalent to a solution of the following equations

Theorems & Definitions (17)

  • lemma thmcounterlemma
  • proof
  • lemma thmcounterlemma
  • theorem 1
  • proof
  • remark thmcounterremark
  • corollary thmcountercorollary
  • theorem 2
  • proof
  • corollary thmcountercorollary
  • ...and 7 more