TARU PUBLICATIONS
Journal of Interdisciplinary Mathematics cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

A modified technique of spectral gradient projection method for solving nonlinear equations systems

* ,

* Corresponding author · click or hover a name for details

pp. 655–665Vol. 27Issue 4June 2024DOI: 10.47974/JIM-1737XML
Received:
12 Sep 2023
Published Online:
31 May 2024
Article type:
Research Article
Language:
EN
Article no.:
JIM-1737
Pages:
655–665

Abstract

This study suggests a new line search algorithm modified of Spectral gradient projection method (SGPM) called (D.A), combining the modified spectral gradient method and projection method for solving nonlinear equations systems. This approach can be more efficient because it requires less CPU time, less function evaluation, and fewer iterations. Furthermore, if this equation is Lipschitz continuous (LC) and monotone, we proved that this technique converges globally. The numerical results show how effective and beneficial this method is for solving nonlinear equations systems.

Keywords

Subject Classifications

34G2034A34

References

[1] H. Masoud, et al., “An Adaptive Nonmonotone Line Search Technique for Solving Systems of Nonlinear Equations.” Journal of Mathematics (2021).
[2] H. H. Dwail and M. A. K. Shiker, ‘’Using trust region method with BFGS technique for solving nonlinear systems of equations,’’ J. Phys.: Conf. Ser. 1818 012022 (2021).
[3] L. H. Hashim, et al., ‘’An application comparison of two Poisson models on zero count data,’’ J. Phys.: Conf. Ser. 1818 012165 (2021).
[4] L. H. Hashim, et al., ‘’An application comparison of two negative binomial models on rainfall count data,’’ J. Phys.: Conf. Ser. 1818 012100 (2021).
[5] K. H. Hashim, et al., “A new line search method to solve the nonlinear systems of monotone equations.” Journal of Engineering and Applied Sciences 14, 10080-10086 (2019).
[6] A. Bouaricha and R.B. Schnabel, “Tensor methods for large sparse systems of nonlinear equations.” Math. Program. 82, 377–400 (1998).
[7] D.W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” SIAM J. Appl. Math. 11, 431–441 (1963).
[8] Y.B. Zhao and D. Li, “Monotonicity of fixed point and normal mappings associated with variational inequality and its application,” SIAM J. Optim. 11, 962–973 (2001).‏
[9] C. T. Kelley, “Iterative methods for linear and nonlinear equations”, Society for Industrial and Applied Mathematics, Philadelphia (1995).
[10] N. K. Dreeb, 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).
[11] M. M. Mahdi, H. H. Dwail, and M. A. K. Shiker, ‘’Hybrid spectral algorithm under a convex constrained to solve nonlinear equations,’’ Journal of Interdisciplinary Mathematics, 25 (5), pp. 1333– 1340 (2022).
[12] H. H. Dwail et al., “A new modified TR algorithm with adaptive radius to solve a nonlinear systems of equations,” J. Phys.: Conf. Ser. 1804 012108 (2021).
[13] B. Jonathan and J. M. Borwein, “Two-point step size gradient methods.” IMA Journal of Numerical Analysis 8.1, 141-148 (1988).
[14] L. Grippo, F. Lampariello, and S. Lucidi, “A nonmonotone line search technique for Newton’s method.” SIAM journal on Numerical Analysis 23.4, 707-716 (1986).‏
[15] L. C. William, and M. Raydan, “Nonmonotone spectral methods for large-scale nonlinear systems.” Optimization Methods and software 18.5, 583-599 (2003).‏ 
[16] L. C. William, J. Martinez, and M. Raydan, “Spectral residual method without gradient information for solving large-scale nonlinear systems of equations.” Mathematics of computation 75.255, 1429-1448 (2006).
[17] L. Zhang and W. Zhou, “Spectral gradient projection method for solving nonlinear monotone equations.” Journal of Computational and Applied Mathematics 196.2 ,478-484 (2006).‏
[18] K. H. Hashim, et al., ‘’Solving the Nonlinear Monotone Equations by Using a New Line Search Technique,’’ J. Phys.: Conf. Ser. 1818 012099 (2021).
[19] M. V. Solodov, and B. F. Svaiter., “A globally convergent inexact Newton method for systems of monotone equations.” Reformulation: Non smooth, piecewise smooth, semi smooth and smoothing methods: 355-369 (1999).
[20] Z. W. Jun and D. H. Li., “A globally convergent BFGS method for nonlinear monotone equations without any merit functions.” Mathematics of Computation 77.264, 2231-224 (2008). 
[21] Shelash, Hader Baqer , Ahmad, Hasanain Hamid & Obaid, Ahmed J.  On characterizations some of subgroups of the dihedral group D2n, Journal of Discrete Mathematical Sciences and Cryptography, 1-6, DOI: 10.47974/JDMSC-1553. 
[22] Shubham Sharma & Ahmed J. Obaid. Mathematical modelling, analysis and design of fuzzy logic controller for the control of ventilation systems using MATLAB fuzzy logic toolbox, Journal of Interdisciplinary Mathematics, 23:4, 843-849 (2020), DOI: 10.1080/09720502.2020.1727611.

Views: 291Downloads: 117Citations: 1