International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3713 2020 2020 Department of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman 11953, Jordan Issam Issam Department of Mathematics, College of Science, Jazan University, Jazan, Saudi Arabia Sultanah Masmali School of Quantitative Sciences, Universiti Utara Malaysia, Sintok, 06010, Kedah, Malaysia; Faculty of Education and Art, Sohar University, Sohar 311, Oman Ibrahim M. Sulaiman Information Systems and Technology Department, Kuwait Technical College, Kuwait Issam A. R. Moghrabi School of Quantitative Sciences, Universiti Utara Malaysia, Sintok, 06010, Kedah, Malaysia Norazura Ahmad Financial Mathematics Program, Faculty of Science and Technology, Universiti Sains Islam Malaysia, Bandar Baru Nilai, 71800, Nilai, Negeri Sembilan, Malaysia Shahrina Ismail 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 2025 258 278 10.54216/IJNS.260220 https://www.americaspg.com/articleinfo/21/show/3713