A Modified Conjugate Gradient Method with Taylor Approximation: Applications in Electric Circuits and Image Restoration
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i1.5639Keywords:
Global convergence;Conjugate gradient method; Unconstrained optimization; Pi-electric circuitAbstract
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.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Ahmad Alhawarat , Sultanah Masmali, Ibtisam Masmali, Mehiddin Al-Baali, Shahrina Ismail

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.
By agreeing to this statement, you acknowledge that:
- You retain full copyright over your work.
- The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
- This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.