aspg-21-3713-1791465314 20261008131514 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2025 26 2 Ahmad Alhawarat Department of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman 11953, Jordan Sultanah Masmali Department of Mathematics, College of Science, Jazan University, Jazan, Saudi Arabia Ibrahim M. Sulaiman School of Quantitative Sciences, Universiti Utara Malaysia, Sintok, 06010, Kedah, Malaysia; Faculty of Education and Art, Sohar University, Sohar 311, Oman Issam A. R. Moghrabi Information Systems and Technology Department, Kuwait Technical College, Kuwait Norazura Ahmad School of Quantitative Sciences, Universiti Utara Malaysia, Sintok, 06010, Kedah, Malaysia Shahrina Ismail Financial Mathematics Program, Faculty of Science and Technology, Universiti Sains Islam Malaysia, Bandar Baru Nilai, 71800, Nilai, Negeri Sembilan, Malaysia In recent years, there has been a surge of attention to the Conjugate Gradient Method (CGM) and its applications. This is because the algorithm of CGM does not require the computation of the second derivative or an approximation during the iteration process. In this study, a four-term descent CGM is proposed by utilizing the famous Polak–Ribiere–Polyak (PRP) conjugate gradient formula. The direction of the proposed method achieves the descent property without line search consideration. In addition, the convergence properties are met to generate the stationary points. Findings from numerical experiments on unconstrained optimization and robotic motion control problems demonstrate that the novel approach outperforms some existing methods including the famous CG-Descent conjugate gradient method. 2025 258 278 3713 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.260220 https://www.americaspg.com/journal/21/article/3713 https://www.americaspg.com/storage/61742001945.pdf