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Simultaneous and semi-alternating projection algorithms for solving split equality problems.

Qiao-Li Dong1, Dan Jiang1

  • 1Tianjin Key Laboratory for Advanced Signal Processing, College of Science, Civil Aviation University of China, Tianjin, 300300 China.

Journal of Inequalities and Applications
|January 26, 2018
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Summary
This summary is machine-generated.

This study introduces novel simultaneous and semi-alternating projection algorithms for solving the split equality problem. These methods demonstrate efficiency and advantages for solving related feasibility problems.

Keywords:
maximal monotone operatorsemi-alternating projection algorithmsimultaneous projection algorithmsplit equality problem

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Area of Science:

  • Optimization Theory
  • Numerical Analysis
  • Applied Mathematics

Background:

  • The split equality problem is a significant challenge in optimization.
  • Existing projection methods have limitations in efficiency and applicability.

Purpose of the Study:

  • To develop and analyze new projection algorithms for the split equality problem.
  • To extend these algorithms to solve the split feasibility problem.
  • To demonstrate the practical efficiency of the proposed methods.

Main Methods:

  • Introduction of two simultaneous projection algorithms with a novel stepsize selection.
  • Proposal of two semi-alternating projection algorithms.
  • Analysis of weak convergence under standard conditions.
  • Application to the split feasibility problem.

Main Results:

  • The proposed simultaneous and semi-alternating projection algorithms effectively solve the split equality problem.
  • Weak convergence of the algorithms is rigorously analyzed.
  • The algorithms are successfully extended to address the split feasibility problem.
  • A numerical example confirms the efficiency and advantages of the developed methods.

Conclusions:

  • The new projection algorithms offer an efficient approach to solving split equality and feasibility problems.
  • The novel stepsize choice enhances algorithm performance.
  • The findings contribute to the advancement of iterative methods in optimization.