A Spectral Conjugate Gradient Method via Hybridization Approach for System of Nonlinear Equations

Authors

  • Abdullahi Adamu Kiri
    Department of General Studies, Jigawa State Polytechnic for Information and Communication Technology Kazaure, Jigawa State, Nigeria
  • Zainab Ishaq
    Department of General Studies, Jigawa State Polytechnic for Information and Communication Technology Kazaure, Jigawa State, Nigeria
  • Zaharaddini Haruna Musa
    Jigawa State College of remedial and advanced studies Babura, Jigawa State , Nigeria
  • Zakari Muhammad
    Department of Sciences, Jigawa State College of Remedial and Advanced Studies, Babura, Jigawa State, Nigeria

Keywords:

System of nonlinear equations, Conjugate gradient parameter, Jacobian matrix, Conjugacy condition, Global convergence

Abstract

This paper present an effective conjugate gradient method via hybridization approach of classical Newton direction and conjugate gradient search direction, the method scheme satisfies the sufficient decent condition. Under mild condition, the global convergence result for the method is established. Preliminary numerical results for some large-scale benchmark test problems reported in this work, demonstrate that, the method is practically effective and competitive to some existing methods. 

Author Biographies

Abdullahi Adamu Kiri

Department of General Studies, Jigawa State Polytechnic for Information and Communication Technology Kazaure, Jigawa State, Nigeria

Zainab Ishaq

Department of General Studies, Jigawa State Polytechnic for Information and Communication Technology Kazaure, Jigawa State, Nigeria

Zakari Muhammad

Department of Sciences, Jigawa State College of Remedial and Advanced Studies, Babura, Jigawa State, Nigeria

 

Dimensions

Abubakar S. H and Muhammad Y. W, (2018): `An improved derivative-free method via double direction approach for solving system of nonlinear equations. J.Ramanujan Maths.Soc.33, Vol. 1, pp 75-89.

Abubakar, S. H and Muhammad Y. W, (2017). A Transformed Double Step Length Method for Solving Large-Scale Systems of Nonlinear Equations. Journal of Numerical Mathematics and Stochastics, 9(1):20-32.

Can Li et al. (2013). A Modi ed Conjugate Gradient Method for Unconstrained Optimization. TELKOMINIKA, vol.11, No.11, pp.6373-6380.

Daud M .K and Mamat H. I., (2019). Hybrid conjugate gradient parameter for solving non-linear equations. Indenusien journal of Electrical Engineering and Computer Science, vol 16, No 1, pp 539-543. 29.

Dexiang F., (2017). A conjugate gradient method update parameter of PRP and YL for solving large scale system of nonlinear equations. Journal of Inequalities and Application. 217-236.

Dauda M K. et al, (2016). In-exact Conjugate Gradient Method via SR1 Update for Solving Systems of Non-linear equations. Far-East Journal of mathematical science (FJMS), vol.100, No.11, pp.1787-1804.

Dola, E, and More J, (2002). A Benchmarking optimization software with performance profiles. Journal of mathematical programming. 91(2), 201-213.

Hamed T. E et al., (2019): A new Hybrid Algorithm for Convex Nonlinear Unconstrained Optimization. Hindawi Journal of applied Mathematics, vol.2019, pp.6.

Jamilu S, Muhammad Y. W, (2017). A New hybrid Dai-Yuan and Hestenes-Stiefel conjugate gradient parameter for solving of non-linear equations. MAYFEB journal of Mathematics, vol.1, pp.441755.

Jamilu S. and Muhammad Y.W, (2017). A new hybrid Dai-Yuan and Hestenes- Stiefel conjugate gradient parameter for solving large scale systems of non-linear equations. MAYFEB journal of mathematics, vol. 1, pages 44-55.

Li D.H. and Fukushima M. A, (2001). A modi_ed BFGS method and its global convergence in non-convex minimization. J. Comput. Appl.Math 129, 15-35.

Mohammad A.H et al., (2014). The Hybrid BFGS-CG Method in Solving Uncontrained optimization Problems. Hindawi pulishing corporation, vol. 2014,pp.6.

Mustafa M, et al., (20014). BFGS-Method: A new search direction. Sains malaysiana, Vol.43, pp.1591-1597.

Mohd A.H et al., (2010). A new search direction of Broyden Conjugate Gradient Method. Far-East Journal of mathematical science (FJMS), vol.101, pp.583-593, No.3.

Tampakas V., (2018). A descent hybrid conjugate gradient method based on the memory-less BFGS update. Cross-Mark, 1075, 018-0497-1.

Sun W and Yuan Y-X, (2006). An optimization theorem and Methods; nonlinear programming. Springer, New York, NY, USA.

Takano. M and Yabe. H, (2004). A globally convergence properties of nonlinear conjugate gradient method via modi_ed secant condition. Comput. optm. Appl. 28(2), 203-225.

Waziri, M Y. and sabiu. J. (2015). A derivative-free conjugate gradient method and its global convergence for symmetric nonlinear equations. Journal of mathematics and mathematical sciences, vol. 2, pp.8.

Waziri M.Y and Kabiru A. (2019). A Dai-Liao conjugate gradient method via modified secant equation for solving non-linear equations. Arabian journal of mathematics, vol 2019, 15-pages.

Yabe, H, and Takano M, (2004). Global convergence properties of new nonlinear conjugate gradient method for unconstrained optimization. Computational optimization and Application, vol.28, pp. 203-225.

Yuan G. and Lu X. (2008). A new backtracking inexact BFGS method for symmetric non-linear equation. Computer and Mathematics with Application, Vol. 55, pp.116-129.

Zhan-Jun S and Jinhua G, (2008). A new algorithm of nonlinear conjugate gradient method with strong convergence. Computational and Applied mathematics, vol.27, No 1, pp.9317106.

Zhan L, Zhou WJ and Li. DH, (2006). Global convergence of a modi_ed Fletcher-Reeves conjugate gradient method with Amirjo-type line search. Numerical Mathematik, 104(4): 561-572.

Zhan.J and Xu.C, (2001). Properties and numerical performance quasi-Newton methods with modi_ed quasi-Newton equations. J Comput. Appl. Math 137(2), 26917278.

Zhen-Jun, S and Jinhua G, (2008). A new algorithm of Nonlinear Conjugate Gradient Method with Strong Convergence. Computational and Applied Mathematics, vol.27, pp.93-106.

Published

2024-12-31

How to Cite

Kiri, A. A., Ishaq, Z., Musa, Z. H., & Muhammad, Z. (2024). A Spectral Conjugate Gradient Method via Hybridization Approach for System of Nonlinear Equations. Journal of Science Research and Reviews, 1(2), 57-62. https://doi.org/10.70882/josrar.2024.v1i2.56

Issue

Vol. 1 No. 2 (2024): JOSRAR Vol. 1 No. 2 (November - December)

Section

Articles
Copyright & Licensing

Copyright (c) 2025 Abdullahi Adamu Kiri, Zainab Ishaq, Zaharaddini Haruna Musa, Zakari Muhammad (Author)

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How to Cite

Kiri, A. A., Ishaq, Z., Musa, Z. H., & Muhammad, Z. (2024). A Spectral Conjugate Gradient Method via Hybridization Approach for System of Nonlinear Equations. Journal of Science Research and Reviews, 1(2), 57-62. https://doi.org/10.70882/josrar.2024.v1i2.56