A Modified Conjugate Gradient Method with Taylor Approximation: Applications in​ Electric Circuits​ and Image Restoration

Authors

  • Ahmad Alhawarat Amman Arab University
  • Sultanah Masmali Jazan University
  • Ibtisam Masmali
  • Mehiddin Al-Baali
  • Shahrina Ismail

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i1.5639

Keywords:

Global convergence;Conjugate gradient method; Unconstrained optimization; Pi-electric circuit

Abstract

In this century, the application of optimization methods is frequently utilized in numerous fields like image restoration, electrical engineering, medical science, machine learning (ML), signal processing as well as many others. In this paper, we choose to improve and maintain one of the most popular, low-memory, and simple algorithms of optimization methods. This method is known as the conjugate gradient method (CGM). Here, we develop a new 3-term CGM with several search directions in the third term suitable for any CGM related to the Fletcher-Reeves method. Apart from that, we propose a new 3-term CGM with mild conditions for any method in relation to the Polak-Ribière-Polyak method. The proposed method satisfies the descent and convergence properties. Moreover, in the numerical findings section, we perform a comparison of the new method with several renowned methods that have emerged in this century, such as CG-Descent 6.8 and nonnegative Dai-Liao methods utilizing more than 180CUTEst library functions. The numerical findings indicate that the novel approach surpasses recent methodologies. These numerical findings encompass the count of gradient assessments, function assessments, CPU duration as well as iteration count. Additionally, we discussed the implementation of the CG method in image restoration and pi-electric circuits.

Author Biography

  • Ahmad Alhawarat , Amman Arab University
    Mathematics

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Published

2025-01-31

Issue

Section

Nonlinear Analysis

How to Cite

A Modified Conjugate Gradient Method with Taylor Approximation: Applications in​ Electric Circuits​ and Image Restoration. (2025). European Journal of Pure and Applied Mathematics, 18(1), 5639. https://doi.org/10.29020/nybg.ejpam.v18i1.5639