A Novel Conjugate Gradient Algorithm for Unconstrained Optimization and Its Application in COVID-19 Data Parameterization

Basim A.  Hassan; Ibrahim Sulaiman Mohammed; Alaa Luqman Ibrahim; Faisal Falah Aiwa

doi:10.21271/ZJPAS.37.3.7

Authors

Basim A. Hassan Department of Mathematics, College of Computers Sciences and Mathematics University of Mosul, Mosul 41002, Iraq
Ibrahim Sulaiman Mohammed 1Institute of Strategic Industrial Decision Modelling, School of Quantitative Sciences, Universiti Utara Malaysia, Sintok 06010, Malaysia ,2 Faculty of Education and Arts, Sohar University, Sohar 311, Oman.
Alaa Luqman Ibrahim Department of Mathematics, College of Science, University of Zakho, Zakho, Kurdistan Region Iraq.
Faisal Falah Aiwa Department of Mathematics, College of Computers Sciences and Mathematics University of Mosul, Mosul 41002, Iraq

DOI:

https://doi.org/10.21271/ZJPAS.37.3.7

Keywords:

Optimization; conjugate gradient Method; Global Convergence; COVID-19

Abstract

To solve unconstrained optimization problems, this study proposes a conjugate gradient (CG) algorithm that satisfies both the convergence and descent conditions. The technique improves on conventional CG techniques through guaranteeing quick convergence and increased solution accuracy across a range of test functions. The study also applies this CG method to model COVID-19 transmission dynamics within a parameterized optimization scope. Analyzing reported cases from January 28, 2024, to September 29, 2024, demonstrates the model's effectiveness in capturing nonlinear trends, with a resurgence of COVID-19 cases in the latter half of the study period. This emphasizes the need for adaptive public health strategies in response to fluctuating infection rates, highlighting the significance of advanced mathematical modeling in infectious disease management.

References

E. Polak and G. Ribiere, “Note sur la convergence de méthodes de directions conjuguées,” Revue française d’informatique et de recherche opérationnelle. Série rouge, vol. 3, no. R1, pp. 35–43, 1969.

Basim A. Hassan and Haneen A. Alashoor, (2023), On image restoration problems using new conjugate gradient methods, Indonesian Journal of Electrical Engineering and Computer Science Vol. 29, No. 3, March 2023, pp. 1438-1445.

M. J. D. Powell, “Nonconvex minimization calculations and the conjugate gradient method,” in Numerical Analysis: Proceedings of the 10th Biennial Conference held at Dundee, Scotland, June 28–July 1, 1983, Springer, 1984, pp. 122–141.

J. C. Gilbert and J. Nocedal, “Global Convergence Properties of Conjugate Gradient Methods for Optimization,” SIAM Journal on Optimization, vol. 2, no. 1, pp. 21–42, 1992, doi: 10.1137/0802003.

S. Shoid et al., “The application of new conjugate gradient methods in estimating data,” International Journal of Engineering and Technology(UAE), vol. 7, no. 2, pp. 25–27, 2018, doi: 10.14419/ijet.v7i2.14.11147.

A. Alhawarat, Z. Salleh, H. Alolaiyan, H. El Hor, and S. Ismail, “A three-term conjugate gradient descent method with some applications,” Journal of Inequalities and Applications, vol. 2024, no. 1, 2024, doi: 10.1186/s13660-024-03142-0.

Z. Chen, H. Shao, P. Liu, G. Li, and X. Rong, “An efficient hybrid conjugate gradient method with an adaptive strategy and applications in image restoration problems,” Applied Numerical Mathematics, vol. 204, pp. 362–379, 2024, doi: https://doi.org/10.1016/j.apnum.2024.06.020.

Basim A. Hassan and Hameed M. Sadiq, (2022), A new formula on the conjugate gradient method for removing impulse noise images, Bulletin of the South Ural State University. Ser. Mathematical Modelling, Programming & Computer Software (Bulletin SUSU MMCS), 2022, vol. 15, no. 4, pp. 123-130.

G. Abbass, H. Chen, M. Abdullahi, and A. B. Muhammad, “An efficient projection algorithm for large-scale system of monotone nonlinear equations with applications in signal recovery,” Journal of Industrial and Management Optimization, vol. 0, no. 0, pp. 0–0, 2024, doi: 10.3934/jimo.2024066.

W. Zhao and H. Huang, “Adaptive stepsize estimation based accelerated gradient descent algorithm for fully complex-valued neural networks,” Expert Systems with Applications, vol. 236, p. 121166, 2024, doi: https://doi.org/10.1016/j.eswa.2023.121166.

H. Iiduka and Y. Kobayashi, “Training deep neural networks using conjugate gradient-like methods,” Electronics (Switzerland), vol. 9, no. 11, pp. 1–25, 2020, doi: 10.3390/electronics9111809.

Basim A. Hassan and Hameed M. Sadiq, (2022), Efficient New Conjugate Gradient Methods for Removing Impulse Noise Images, Europear Journal of Pure and Applied Mathematics, Vol. 15, No. 4, 2011-2021.

A. L. Ibrahim and M. G. Mohammed, “A new conjugate gradient for unconstrained optimization problems and its applications in neural networks,” Indonesian Journal of Electrical Engineering and Computer Science, vol. 33, no. 1, pp. 93–100, 2024, doi: 10.11591/ijeecs.v33.i1.pp93-100.

B. A. Hassan and A. Ahmed A. Abdulla, “Improvement of conjugate gradient methods for removing impulse noise images,” Indonesian Journal of Electrical Engineering and Computer Science, vol. 29, p. 245, 2022, doi: 10.11591/ijeecs.v29.i1.pp245-251.

G. Zoutendijk, “Nonlinear Programming Computational Methods,” In: Abadie, J. Ed., Integer and Nonlinear Programming, NorthHolllad, Amsterdam, pp. 37-86., 1970.

N. I. M. Gould, D. Orban, and P. L. Toint, “CUTEr and sifdec: A constrained and unconstrained testing environment, revisited,” ACM Transactions on Mathematical Software, vol. 29, no. 4, pp. 373–394, 2003, doi: 10.1145/962437.962439.

J. J. Moré, B. S. Garbow, and K. E. Hillstrom, “Testing Unconstrained Optimization Software,” ACM Transactions on Mathematical Software (TOMS), vol. 7, no. 1, pp. 17–41, 1981, doi: 10.1145/355934.355936.

N. Andrei, “An unconstrained optimization test functions collection,” Advanced Modelling and Optimization, vol. 10, no. 1, pp. 147–161, 2008.

E. D. Dolan and J. J. Moré, “Benchmarking optimization software with performance profiles,” Mathematical Programming, vol. 91, no. 2, pp. 201–213, 2002, doi: 10.1007/s101070100263.

World Health Organization: https://data.who.int/dashboards/covid19/cases.

I. M. Sulaiman, M. Malik, A. M. Awwal, P. Kumam, M. Mamat, and S. Al-Ahmad, “On three-term conjugate gradient method for optimization problems with applications on COVID-19 model and robotic motion control.,” Advances in continuous and discrete models, vol. 2022, no. 1, p. 1, 2022, doi: 10.1186/s13662-021-03638-9.