TARU PUBLICATIONS
Journal of Interdisciplinary Mathematics cover
Hybrid ·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

New conjugate gradient methods based on the modified secant condition

, , , , *

* Corresponding author · click or hover a name for details

pp. 19–30Vol. 28Issue 1February 2025DOI: 10.47974/JIM-1771XML
Received:
11 Jun 2024
Published Online:
13 Feb 2025
Article type:
Research Article
Language:
EN
Article no.:
JIM-1771
Pages:
19–30

Abstract

Conjugate gradient (CG) algorithms are an optimization method with fast convergence. To date, several CG methods have been developed to improve computational performance and have been used to solve unconstrained optimization problems. In this paper, a new CG algorithm based on the modified secant condition is proposed to solve unconstrained optimization problems. The proposed algorithm has the following properties:it achieves sufficient descent property and global convergence property, We used a number of test functions for large-scale unconstrained optimization problems and the numbers showed that the proposed algorithm works better than other algorithms like Hestenes and Steifel (HS) and Fletcher and Revees (FR).

Keywords

Subject Classifications

90C3065K0549M37

References

[1] H. M. Khudhur and A. A. M. Fawze. An improved conjugate gradient method for solving unconstrained optimisation and image restoration problems. Int. J. Math. Model. Numer. Optim., vol. 13, no. 3, pp. 313-325 (2023), https://doi.org/10.1504/IJMMNO.2023.132286.
[2] Y. A. Laylani, B. A. Hassan and H. M. Khudhur. Enhanced spectral conjugate gradient methods for unconstrained optimization. Comput. Sci., vol. 18, no. 2, pp. 163-172 (2023).
[3] H. N. Jabbar and B. A. Hassan. Two-versions of descent conjugate gradient methods for large-scale unconstrained optimization. Indonesian Journal of Electrical Engineering and Computer Science, vol. 22, no. 3 (2021), https://doi.org/10.11591/ijeecs.v22.i3.pp1643-1649.
[4] R. Fletcher. Function minimization by conjugate gradients. Comput. J., vol. 7, no. 2, pp. 149-154, Feb. (1964), https://doi.org/10.1093/comjnl/7.2.149.
[5] S. M. Kadham, “Acute interstitial pneumonia image enhancement using fuzzy partial transforms,” Applied Geomatics, vol. 16, no. 1, pp. 35–39 (May 2023), doi: https://doi.org/10.1007/s12518-023-00509-8.
[6] M. R. Hestenes and E. Stiefel. Methods of conjugate gradients for solving linear systems. J. Res. Natl. Bur. Stand. (1934)., vol. 49, no. 6, pp. 409-436, Dec. (1952), https://doi.org/10.6028/jres.049.044.
[7] L. Mahdi, H.W. Mahdi, and Q. L. Abdulrasool, “Mechanical Properties of Waste Aggregate-Steel Fiber Reinforced Concrete Modified with Water prof Admixture,” International Journal of Civil Engineering and Technology (IJCIET), vol. 9, no. 11, pp. 934–947, 2018, Accessed: Jan. 28 (2025).
[8] Y. H. Dai and Y. Yuan. A nonlinear conjugate gradient method with a strong global convergence property. SIAM J. Optim., vol. 10, no. 1, pp. 177-182 (1999), https://doi.org/10.1137/S1052623497318992.
[9] R. Fletcher, Unconstrained Optimization Practical Methods of Optimization, vol. 1. New York:Wiley (1987).
[10] B.A. Hassan, M. Malik and I.M. Sulaiman. A variant of Dai-Yuan conjugate gradient method for unconstrained optimization and its application in portfolio selection. J. Math. Comput. Sci. (2021), https://doi.org/10.28919/jmcs/5798.
[11] B. A. Hassan, Z. M. Abdullah and H. N. Jabbar. A descent extension of the Dai - Yuan conjugate gradient technique. Indonesian Journal of Electrical Engineering and Computer Science, vol. 16, no. 2 (2019), https://doi.org/10.11591/ijeecs.v16.i2.pp661-668.
[12] I. M. Sulaiman, N. A. Bakar, M. Mamat, B. A. Hassan, M. Malik and A. M. Ahmed. A new hybrid conjugate gradient algorithm for optimization models and its application to regression analysis. Indones. J. Electr. Eng. Comput. Sci., vol. 23, no. 2, pp. 1100, Aug. (2021), https://doi.org/10.11591/ijeecs.v23.i2.pp1100-1109.
[13] S. Aji, P. Kumam, P. Siricharoen, A. B. Abubakar, M. M. Yahaya. A Modified Conjugate Descent Projection Method for Monotone Nonlinear Equations and Image Restoration. IEEE Access, vol. 8, pp. 158656-158665 (2020), https://doi.org/10.1109/ACCESS.2020.3020334.
[14] Y. Dai, J. Han, G. Liu, D. Sun, H. Yin and Y. Yuan. Convergence Properties of Nonlinear Conjugate Gradient Methods. SIAM J. Optim., vol. 10, no. 2, pp. 345-358, Jan. (2000), DOI:10.1137/S1052623494268443.
[15] N. I. M. Gould, D. Orban and P. L. Toint. CUTEr and SifDec:A constrained and unconstrained testing environment, revisited. ACM Trans. Math. Softw., vol. 29, no. 4, pp. 373-394, Dec. (2003), https://doi.org/10.1145/962437.962439.
[16] J. J. Moré, B. S. Garbow and K. E. Hillstrom. Testing unconstrained optimization software. ACM Trans. Math. Softw., vol. 7, no. 1, pp. 17-41 (1981).
[17] R. A. Kamil, H. M. Atiea, A. A. Kadhem, Layth Abdulrasool Alasadi, and Q. A. Jabal, “Improvement of the mechanical properties of polymer-modified concrete by using PC superplasticizer,” Pollack Periodica, vol. 18, no. 3, pp. 14–19 (Jul. 2023), doi: https://doi.org/10.1556/606.2023.00742.
[18] B. Sellami, Y. Laskri and R. Benzine. A new two-parameter family of nonlinear conjugate gradient methods. Optimization, vol. 64 (2015).
[19] E. D. Dolan and J. J. Moré. Benchmarking optimization software with performance profiles. Math. Program. Ser. B, vol. 91, no. 2, pp. 201-213 (2002), https://doi.org/10.1007/s101070100263.
[20] W. Gao and M. R. Farahani. The hyper-zagreb index for an infinite family of nanostar dendrimer,” J. Discrete Math. Sci. Cryptography, vol. 20, no. 2, pp. 2017, https://doi.org/10.1080/09720529.2016.1220088.
[21] M. Imran, A. A. E. Abunamous, D. Adi, S. H. Rafique, A. Q. Baig and M. R. Farahani. Eccentricity based topological indices of honeycomb networks.,” J. Discrete Math. Sci. Cryptography, vol. 22, no. 7, pp. 2019, https://doi.org/10.1080/09720529.2019.1691326.

[22] W. Gao and M. R. Farahani. The hyper-zagreb index for an infinite family of nanostar dendrimer,” J. Discrete Math. Sci. Cryptography, vol. 20, no. 2, pp. 2017, https://doi.org/10.1080/09720529.2016.1220088.
[23] M. Imran, A. A. E. Abunamous, D. Adi, S. H. Rafique, A. Q. Baig and M. R. Farahani. Eccentricity based topological indices of honeycomb networks.,” J. Discrete Math. Sci. Cryptography, vol. 22, no. 7, pp. 2019, https://doi.org/10.1080/09720529.2019.1691326.
[24] W. Gao, L. Shi and M. R. Farahani. Szeged Related Indices of TUAC6[p,q],” J. Discrete Math. Sci. Cryptography, vol. 20, no. 2, pp. 2017, https://doi.org/10.1080/09720529.2016.1228312.
[25] S. Ahmad, H. M. A. Siddiqui, A. Ali, M. R. Farahani, M. Imran and I. N. Cangul. On Wiener index and Wiener polarity index of some poly­omino chains,” J. Discrete Math. Sci. Cryptography, vol. 22, no. 7, pp. 2019, https://doi.org/10.1080/09720529.2019.1688965.
[26] M. Nadeem, S. Ahmad, M. K. Siddiqui, M. A. Ali, M. R. Farahani and A. J. M. Khalaf. On some applications related with algebraic structures through different well known graphs,” J. Discrete Math. Sci. Cryptog­raphy, vol. 24, no. 2, pp. 2021, https://doi.org/10.1080/09720529.2021.1885806.

Views: 252Downloads: 86Citations: 0