A modified (CG) method for solving nonlinear systems of monotone equations

Habib, Hussein Saad; Shiker, Mushtak A. K.

doi:10.47974/JIM-1872

Open Access Research Article

A modified (CG) method for solving nonlinear systems of monotone equations

^*Hussein Saad HabibCorresponding authorpure304.hussien.saad@student.uobabylon.edu.iqDepartment of Mathematics College of Education for Pure Sciences University of BabylonDepartment of Mathematics College of Education for Pure Sciences University of Babylon Hilla, Babylon, IraqView full profile → , Mushtak A. K. Shikerpure.mushtaq@uobabylon.edu.iqDepartment of Mathematics College of Education for Pure Sciences University of BabylonDepartment of Mathematics College of Education for Pure Sciences University of Babylon Hilla, Babylon, IraqView full profile →

* Corresponding author · click or hover a name for details

pp. 787–792Vol. 27Issue 4June 2024DOI: 10.47974/JIM-1872XML

Received:: 13 Dec 2023
Published Online:: 30 Jun 2024
Article type:: Research Article
Language:: EN
Article no.:: JIM-1872
Pages:: 787–792

Abstract

In this paper, a new modified of conjugate gradient method named the (HSH) algorithm is presented for solving nonlinear systems of monotone equations (NSME). The main goal is the (HSH) technique can decrease the number of iterations (Ni), the CPU-time (NT), and the number of functions evaluation(Nf), by MATLAB R_2020a and a numerical results comparison with SCG method and PRP method. Under some standard conditions, the well- define and the convergence of the (HSH) algorithm are proved. The numerical experiment indicated the efficiency of the (HSH).

Keywords

Nonlinear systems Conjugate gradient method (CGM)Global convergence

Subject Classifications

46N1047N1090C30

References

[1] Ou, Y. & Jingya, L., A new derivative-free SCG-type projection method for nonlinear monotone equations with convex constraints, Journal of Applied Mathematics and Computing, 56, pp. 195-216 (2018).
[2] Cheng, W., A PRP type method for systems of monotone equations, Mathematical and Computer Modeling, 50:2, pp. 15-20 (2009).
[3] Guo, J., & Zhong, W., A modified spectral PRP conjugate gradient projection method for solving large-scale monotone equations and its application in compressed sensing, Mathematical Problems in Engineering (2019).‏
[4] Wan, Z., Zhan, L. Y., & YaLin, W., New spectral PRP conjugate gradient method for unconstrained optimization, Applied Mathematics Letters, 24:1, pp. 16- 22 (2011).
[5] Dwail, H. H. et al., A new modified TR algorithm with adaptive radius to solve a nonlinear systems of equations, J. Phys.: Conf. Ser. 1804 012108 (2021).
[6] Mohammed, A. M. & Al- Khafaji, Z., Innovative way to evaluate the reliability and importance of complex- series networks, 6th International Conference on Engineering Technology and its Applications (IICETA), Al-Najaf, Iraq, pp. 540- 544 (2023).
[7] Dreeb, N. K. et al., Using a New Projection Approach to Find the Optimal Solution for Nonlinear Systems of Monotone Equation, J. Phys.: Conf. Ser. 1818 012101 (2021).
[8] Alridha, F. A. W. & Kadhim, M. K. Training analysis of optimization models in machine learning, International Journal of Nonlinear Analysis and Applications, 12: 2, pp. 1453-1461 (2021).
[9] Mahdi, M. M., Hadi, D. H., & Shiker, M. A. K., Hybrid spectral algorithm under a convex constrained to solve nonlinear equations, Journal of Interdisciplinary Mathematics, 25: 5, pp. 1333– 1340 (2022).
[10] Saleh, A. A. H. & Hassan, Z. A. H. Improve the mixed system’s reliability, In AIP Conference Proceedings, 2834: 1, AIP Publishing (2023).
[11] Mahdi, M. M. et al., Solving systems of nonlinear monotone equations by using a new projection approach, J. Phys.: Conf. Ser. 1804 012107 (2021).
[12] Hussein, Y. A. & Shiker, M. A. K., Using the largest difference method to find the initial basic feasible solution to the transportation problem, Journal of Interdisciplinary Mathematics, 25: 8, pp. 2511-2517 (2022).
[13] Abbas, S. A. K. & Hassan, Z. A. H., Use of ARINC Approach method to evaluate the reliability assignment for mixed system, Journal of Physics: Conference Series, 1999:1, 012102 (2021).
[14] Dwail, H. , Maad, M. M., & Shiker, M. A. K., CG method with modifying β_k for solving unconstrained optimization problems, Journal of Interdisciplinary Mathematics, 25: 5, pp. 1347– 1355 (2022).
[15] Karrar, H. H. et al., Solving the Nonlinear Monotone Equations by Using a New Line Search Technique, J. Phys.: Conf. Ser. 1818 012099 (2021).
[16] Salman, A. M., Alridha, A. & Hussain, A. H. Some topics on convex optimization, J. Phys. Conf. Ser., 1818: 1, 012171 (2021).
[17] Laith. H. et al., An application comparison of two Poisson models on zero count data, J. Phys.: Conf. Ser. 1818 012165 (2021).
[18] Mohammed, A. M. & Al- Khafaji, Z. Novel approach to obtain minimum path cut sets for complex- series networks, 6th International Conference on Engineering Technology and its Applications (IICETA), Al-Najaf, Iraq, pp. 659- 664 (2023).
[19] Hashim, L. et al., An application comparison of two negative binomial models on rainfall count data, J. Phys.: Conf. Ser. 1818 012100 (2021).
[20] Al-Ameedee, Sarah A. & Obaid, Ahmed J. Sandwich results of meromorphic multivalent functions defined by multiplier transform, Journal of Interdisciplinary Mathematics (2023), OnlineFirst : Latest Articles, 1-8, DOI: 10.47974/JIM-1484.
[21] Abbood, Mohaimen M., Ebrahim, Hassan H., Al-Fayadh, Ali & Obaid, Ahmed J. Measure defined on Γ–algebra and some of their generalizations, Journal of Interdisciplinary Mathematics, 1-7, DOI: 10.47974/JIM-1502.

Views: 139Downloads: 6Citations: 1