On three-term conjugate gradient method for optimization problems with applications on COVID-19 model and robotic motion control

Ibrahim Mohammed Sulaiman; Maulana Malik; Aliyu Muhammed Awwal; Poom Kumam; Mustafa Mamat; Shadi Al-Ahmad

doi:10.1186/s13662-021-03638-9

On three-term conjugate gradient method for optimization problems with applications on COVID-19 model and robotic motion control

Adv Contin Discret Model. 2022;2022(1):1. doi: 10.1186/s13662-021-03638-9. Epub 2022 Jan 4.

Authors

Ibrahim Mohammed Sulaiman¹, Maulana Malik², Aliyu Muhammed Awwal^{3

4

5}, Poom Kumam^{4

5

6}, Mustafa Mamat⁷, Shadi Al-Ahmad⁷

Affiliations

¹ Department of Mathematics and Statistics, School of Quantitative Sciences, College of Art and Sciences (CAS), Universiti Utara Malaysia (UUM), 06010 Sintok, Kedah Malaysia.
² Department of Mathematics, Universitas Indonesia (UI), Depok, 16424 Indonesia.
³ Department of Mathematics, Faculty of Science, Gombe State University, Gombe, Nigeria.
⁴ Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok, 10140 Thailand.
⁵ KMUTT-Fixed Point Theory and Applications Research Group, Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok, 10140 Thailand.
⁶ Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402 Taiwan.
⁷ Faculty of informatics and Computing, Universiti Sultan Zainal Abidin (UniSZA), Terengganu, 22200 Malaysia.

Abstract

The three-term conjugate gradient (CG) algorithms are among the efficient variants of CG algorithms for solving optimization models. This is due to their simplicity and low memory requirements. On the other hand, the regression model is one of the statistical relationship models whose solution is obtained using one of the least square methods including the CG-like method. In this paper, we present a modification of a three-term conjugate gradient method for unconstrained optimization models and further establish the global convergence under inexact line search. The proposed method was extended to formulate a regression model for the novel coronavirus (COVID-19). The study considers the globally infected cases from January to October 2020 in parameterizing the model. Preliminary results have shown that the proposed method is promising and produces efficient regression model for COVID-19 pandemic. Also, the method was extended to solve a motion control problem involving a two-joint planar robot.

Keywords: Coronavirus (COVID-19); Finite difference; Line search procedure; Motion control; Optimization models; Regression analysis; Three-term CG algorithms.