TARU PUBLICATIONS
Journal of Information and Optimization Sciences cover

Journal of Information and Optimization Sciences

(Since 1980)
Hybrid ·Peer-reviewed·ISSN (Online): 2169-0103·ISSN (Print): 0252-2667

WoS  JIF 2026 : 0.4 (Q4)

Powered by:Powered by

Monthly Journal: Publishes theoretical and applied research on topics in information and optimization sciences.

Issues up to 2022 co-published with and available at:Taylor & Francis
submissions@tarupublications.com
Taru Online First Current IssueSpecial IssuesBrowse all Issues
Journal of Information and Optimization Sciences
Open Access Research Article

A new parameter to enhance three-term conjugate gradient method with inexact line search

* ,

* Corresponding author · click or hover a name for details

pp. 717–727Vol. 46Issue 3April 2025DOI: 10.47974/JIOS-1770XML
Received:
08 Nov 2023
Published Online:
31 Mar 2025
Article type:
Research Article
Language:
EN
Article no.:
JIOS-1770
Pages:
717–727

Abstract

This Work presents a new parameter for the gradient of the three-term conjugate called (TTFGH) method, the 3T-CG algorithms are quite popular for solving large-scale unconstrained problems Due to their appealing practical qualities, such as their computational simplicity, Strong global convergence properties, better descent property, and reduced memory requirements. By employing Wolfe-Powell (sWP) line search condition, these newly developed methods always satisfy the original condition. The proposed approaches’ global convergence characteristics are indicated by sWP, assuming Lipschitzian continuity of the objective function. Based on numerical results and preliminary comparisons with the of the modern methods, the proposed methods show that they are effective and promising.

Keywords

Conjugate gradientThree termAdequate descent property(sWP) line search

Subject Classifications

65K0590C0690C3090C5290C56

References

[1] G. M. Al-Naemi and A. H. Sheekoo, “New scaled algorithm for non-linear conjugate gradients in unconstrained optimization,” Indonesian Journal of Electrical Engineering and Computer Science, vol. 24, no. 3, pp. 1589-1595 (2021).
[2] G. M. Al-Naemi, “A new modified HS algorithm with strong Powell-Wolfe line search for unconstrained optimization,” Eastern-European Journal of Enterprise Technologies, vol. 116, no. 2, pp. 14-21 (2022).
[3] N. Andrei, “An unconstrained optimization test functions collection,” Advanced Modeling and Optimization, vol. 10, no. 1, pp. 147-161 (2008).
[4] N. Andrei, “Test functions for unconstrained optimization,” Research Institute for Informatics, Center for Advanced Modeling and Optimization, pp. 8-10 (2004).
[5] B. Baluch, Z. Salleh, A. Alhawarat, and U. A. M. Roslan, “A new modified three-term conjugate gradient method with sufficient descent property and its global convergence,” Journal of Mathematics (2017).
[6] E. M. L. Beale, “A derivation of conjugate gradient,” in F. A. Lootsma, Ed., Numerical Methods for Nonlinear Optimization. London: Academic Press, pp. 39–43 (1972).
[7] I. Bongartz, A. R. Conn, N. Gould, and P. L. Toint, “CUTE: Constrained and unconstrained testing environment,” ACM Transactions on Mathematical Software (TOMS), vol. 21, no. 1, pp. 123-160 (1995).
[8] Y. H. Dai and Y. Yuan, “A nonlinear conjugate gradient method with a strong global convergence property,” SIAM Journal on Optimization, vol. 10, no. 1, pp. 177-182 (1999).
[9] E. D. Dolan and J. J. Moré, “Benchmarking optimization software with performance profiles,” Mathematical Programming, vol. 91, no. 2, pp. 201-213 (2002).
[10] N. H. Fadhila, M. Rivaie, F. Ishak, and N. Idalisa, “New three-term conjugate gradient method with exact line search,” MATEMATIKA: Malaysian Journal of Industrial and Applied Mathematics, vol. 36, no. 3, pp. 197-207 (2020).
[11] R. Fletcher, Practical Methods of Optimization. New York: John Wiley & Sons (1987).
[12] R. Fletcher and C. Reeves, “Function minimization by conjugate gradients,” Comput. J., vol. 7, pp. 149-154 (1964).
[13] W. W. Hager and H. Zhang, “A new conjugate gradient method with guaranteed descent and an efficient line search,” SIAM Journal on Optimization, vol. 16, no. 1, pp. 170-192 (2005).
[14] A. Hallal, M. Belloufi, and B. Sellami, “Using a new hybrid conjugate gradient method with descent property,” Journal of Information & Optimization Sciences, vol. 44, no. 7, pp. 1287-1302 (2023).
[15] M. R. Hestenes and E. Stiefel, “Methods of conjugate gradients for solving linear systems,” Journal of Research of the National Bureau of Standards, vol. 2, pp. 14-21 (1952).
[16] N. Idalisa, M. Rivaie, N. H. M. Noh, M. A. S. Nasir, N. H. Fadhilah, and N. Alias, “A new three-term conjugate gradient method with application to regression analysis,” International Journal of Electrical & Computer Engineering, vol. 12, no. 5, pp. 2088-8708 (2022).
[17] F. N. Jardow and G. M. Al-Naemi, “A new hybrid conjugate gradient algorithm for unconstrained optimization with inexact line search,” Indonesian Journal of Electrical Engineering and Computer Science, vol. 20, pp. 939-947 (2020).
[18] J. Liu and X. Wu, “New three-term conjugate gradient method for solving unconstrained optimization problems,” Science Asia, vol. 40, no. 4, pp. 295-300 (2014).
[19] P. Mtagulwa and P. Kaelo, “A convergent modified HS-DY hybrid conjugate gradient method for unconstrained optimization problems,” Journal of Information and Optimization Sciences, vol. 40, no. 1, pp. 97-113 (2019).
[20] H. Y. Najm and H. I. Ahmed, “Conjugate gradient method for solving unconstrained optimization problems: A new investigation and application,” Journal of Interdisciplinary Mathematics, vol. 26, no. 4, pp. 601–611 (2023).
[21] P. Wolfe, “Convergence conditions for ascent methods,” Mathematical Programming, vol. 11, no. 2, pp. 226-233 (1969).
[22] 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. 16, pp. 35-43 (1969).
[23] B. T. Polyak, “The conjugate gradient method in extremal problems,” USSR Computational Mathematics and Mathematical Physics, vol. 9, no. 4, pp. 94-112 (1969).
[24] M. Rivaie, M. Mamat, L. W. June, and I. Mohd, “A new class of nonlinear conjugate gradient coefficients with global convergence properties,” Applied Mathematics and Computation, vol. 2189, pp. 11323-11332 (2012).
[25] I. M. Sulaiman, M. Mamat, A. E. Owoyemi, P. L. Ghazali, M. Rivaie, and M. Malik, “The convergence properties of some descent conjugate gradient algorithms for optimization models,” Journal of Mathematics and Computer Science, vol. 22, no. 3, pp. 204-215 (2020).
[26] Y. H. Dai and L. Z. Liao, “New conjugacy conditions and related nonlinear conjugate gradient methods,” Applied Mathematics and Optimization, vol. 43, pp. 87-101 (2001).
[27] J. Zhang, Y. Xiao, Z. Wei, and J. Júdice, “Nonlinear conjugate gradient methods with sufficient descent condition for large-scale unconstrained optimization,” Mathematical Problems in Engineering (2009).
[28] L. Zhang, W. Zhou, and D. Li, “Some descent three-term conjugate gradient methods and their global convergence,” Optimization Methods and Software, vol. 22, no. 4, pp. 697–711 (2007).
[29] L. Zhang, W. Zhou, and D. H. Li, “A descent modified Polak–Ribière–Polyak conjugate gradient method and its global convergence,” IMA Journal of Numerical Analysis, vol. 26, no. 4, pp. 629-640 (2006).
[30] G. Zoutendijk, “Nonlinear programming, computational methods, Integer and nonlinear programming,” in J. Abadie, Ed., Integer and Nonlinear Programming. Amsterdam: North-Holland, pp. 37-86 (1970).

Views: 299Downloads: 55Citations: 0