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An algorithm for the split-feasibility problems with application to the split-equality problem.

Chih-Sheng Chuang1, Chi-Ming Chen2

  • 1Department of Applied Mathematics, National Chiayi University, Chiayi, Taiwan.

Journal of Inequalities and Applications
|December 16, 2017
PubMed
Summary
This summary is machine-generated.

This study introduces a projected reflected gradient algorithm for solving split-feasibility problems in Hilbert spaces. New algorithms are presented for convex linear inverse and split-equality problems, with supporting numerical results.

Keywords:
linear inverse problemprojectionsplit-equality problemsplit-feasibility problem

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Area of Science:

  • Optimization theory
  • Functional analysis
  • Numerical analysis

Background:

  • Split-feasibility problems (SFPs) are fundamental in optimization and signal processing.
  • Existing methods for SFPs in Hilbert spaces have limitations.
  • Convex linear inverse problems and split-equality problems are important applications.

Purpose of the Study:

  • To develop and analyze a novel projected reflected gradient algorithm for solving SFPs in Hilbert spaces.
  • To extend the application of this algorithm to convex linear inverse problems and split-equality problems.
  • To provide new algorithmic solutions for these related problems.

Main Methods:

  • The projected reflected gradient algorithm is utilized.
  • Theoretical analysis of convergence properties is performed.
  • Numerical experiments are conducted to validate the algorithms.

Main Results:

  • The proposed algorithm demonstrates effectiveness for SFPs in Hilbert spaces.
  • New algorithms are successfully developed for convex linear inverse and split-equality problems.
  • Numerical results confirm the performance and applicability of the presented methods.

Conclusions:

  • The projected reflected gradient algorithm offers a viable approach for SFPs.
  • The study contributes new algorithms and insights into related inverse and equality problems.
  • The findings have potential implications for various fields utilizing optimization techniques.