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ORIGINAL RESEARCH article

Front. Appl. Math. Stat.
Sec. Optimization
Volume 11 - 2025 | doi: 10.3389/fams.2025.1477774

Numerical Optimization of Large-Scale Monotone Equations Using the Free-Derivative Spectral Conjugate Gradient Method

Provisionally accepted
Ghulam Abbass Ghulam Abbass 1Nek Muhammad Katbar Nek Muhammad Katbar 1Israr Ahmed Memon Israr Ahmed Memon 2Fikadu Tesgera Tolasa Fikadu Tesgera Tolasa 3*
  • 1 Central South University, Changsha, China
  • 2 Shah Abdul Latif University, Khairpur, Sindh, Pakistan
  • 3 Dambi Dollo University, Dambi Dollo, Ethiopia

The final, formatted version of the article will be published soon.

    This study introduced an efficient method for solving non-linear equations. Our approach enhances the traditional spectral conjugate gradient parameter, resulting in significant improvements in the resolution of complex nonlinear problems. This innovative technique ensures global convergence and descent condition supported by carefully considered assumptions. The efficiency and effectiveness of the proposed method is highlighted by its outstanding numerical performance. To validate our claims, large-scale numerical simulations were conducted. These tests were designed to evaluate the capabilities of our proposed algorithm rigorously. In addition, we performed a comprehensive comparative numerical analysis, benchmarking our method against existing techniques. This analysis revealed that our approach consistently outperformed others in terms of theoretical robustness and numerical efficiency. The superiority of our method is evident in its ability to solve large-scale problems with accuracy in function evaluations, fewer iterations, and improved computational performance thereby, making it a valuable contribution to the field of numerical optimization.

    Keywords: Non-linear Equation, convex constraints, Monotone operator, Global convergence, spectral parameter

    Received: 08 Aug 2024; Accepted: 08 Jan 2025.

    Copyright: © 2025 Abbass, Katbar, Memon and Tolasa. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

    * Correspondence: Fikadu Tesgera Tolasa, Dambi Dollo University, Dambi Dollo, Ethiopia

    Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.