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An innovative inertial extra-proximal gradient algorithm for solving convex optimization problems with application to

Joshua Olilima1, Adesanmi Mogbademu2, M Asif Memon3

  • 1Department of Mathematical Sciences, Augustine University, Ilara-Epe, Lagos, Nigeria.

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|October 9, 2023
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Summary
This summary is machine-generated.

Researchers developed a novel self-adaptive extra proximal algorithm with an inertial term for convex optimization. This method enhances image deblurring and signal reconstruction, even with limited data, improving optimization outcomes.

Keywords:
Convex minimization problemForward-backward algorithmInertial methodSignal & image processingWeak convergence

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Area of Science:

  • Optimization Theory
  • Applied Mathematics
  • Image and Signal Processing

Background:

  • Convex optimization problems are prevalent in image and signal processing.
  • Existing methods may face challenges with convergence speed and efficiency.
  • Advanced optimization techniques are crucial for complex reconstruction tasks.

Purpose of the Study:

  • To introduce a novel self-adaptive extra proximal algorithm for convex optimization.
  • To incorporate an inertial term to accelerate convergence.
  • To demonstrate the algorithm's efficacy in image deblurring and signal reconstruction.

Main Methods:

  • Development of a self-adaptive extra proximal algorithm.
  • Inclusion of an inertial term within the optimization framework.
  • Rigorous convergence analysis and numerical validation.

Main Results:

  • The proposed algorithm shows effectiveness in image deblurring and signal reconstruction.
  • Successful application using only 10% of the original signal data.
  • Demonstrated potential for faster convergence compared to existing methods.

Conclusions:

  • The novel algorithm offers an effective approach to convex optimization problems.
  • The inertial term significantly enhances convergence and optimization performance.
  • This research advances optimization techniques for practical image and signal processing applications.