A Descent Conjugate Gradient Method for Large Scale Unconstrained Optimization Problems with Application

Ahmad Alhawarat¹, Sultanah Masmali², Ibrahim M. Sulaiman^{3, 4}, Issam A. R. Moghrabi^5,*, Norazura Ahmad³, Shahrina Ismail⁶

¹Department of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman 11953, Jordan

²Department of Mathematics, College of Science, Jazan University, Jazan, Saudi Arabia

³School of Quantitative Sciences, Universiti Utara Malaysia, Sintok, 06010, Kedah, Malaysia

⁴Faculty of Education and Art, Sohar University, Sohar 311, Oman

⁵Information Systems and Technology Department, Kuwait Technical College, Kuwait

⁶Financial Mathematics Program, Faculty of Science and Technology, Universiti Sains Islam Malaysia, Bandar Baru Nilai, 71800, Nilai, Negeri Sembilan, Malaysia

Emails: abadee2010@yahoo.com; sultanah@math.ksu.edu; sulaimancga@gmail.com; i.moghrabi@ktech.edu.kw; nhaslinda@ummaed.my

Abstract

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.

Keywords: Inexact line search; Conjugate gradient method; Descent condition; CG-Descent; Numerical comparison