An improved conjugate gradient algorithm by adapting a new line search technique

Asma Maiza; Raouf Ziadi; Mohammed A. Saleh; Abdulgader Z. Almaymuni; Asma Maiza; Raouf Ziadi; Mohammed A. Saleh; Abdulgader Z. Almaymuni

doi:10.3934/era.2025094

Electronic Research Archive

2025, Volume 33, Issue 4: 2148-2171. doi: 10.3934/era.2025094

Previous Article Next Article

Research article

An improved conjugate gradient algorithm by adapting a new line search technique

1.
Laboratory of Fundamental and Numerical Mathematics (LMFN), Department of Mathematics, University Setif-1-Ferhat Abbas, Setif, Algeria
2.
Department of Cybersecurity, College of Computer, Qassim University, Saudi Arabia

Received: 03 December 2024 Revised: 17 March 2025 Accepted: 27 March 2025 Published: 15 April 2025

The conjugate gradient (CG) method is an optimization technique known for its rapid convergence; it has blossomed into significant developments and applications. Numerous variations of CG methods have emerged to enhance computational efficiency and address real-world challenges. This work presents a new conjugate gradient method for solving nonlinear unconstrained optimization problems by introducing a new conjugate gradient parameter. To improve the convergence properties, we have proposed a new inexact line search technique that fits in with the suggested approach and can also be useful for other gradient descent methods. The existence of a steplength that meets the new line search conditions is established. The generated descent direction and the convergence properties of the suggested approach are studied under the new line search conditions, where the global convergence is proven under mild assumptions. The proposed approach is evaluated on various test functions, and a comparison with recent similar algorithms is carried out. Furthermore, the proposed algorithm is applied for restoring images with different noise levels.

Keywords:

Citation: Asma Maiza, Raouf Ziadi, Mohammed A. Saleh, Abdulgader Z. Almaymuni. An improved conjugate gradient algorithm by adapting a new line search technique[J]. Electronic Research Archive, 2025, 33(4): 2148-2171. doi: 10.3934/era.2025094

Related Papers:

[1]	Andro Mikelić, Giovanna Guidoboni, Sunčica Čanić . Fluid-structure interaction in a pre-stressed tube with thick elastic walls I: the stationary Stokes problem. Networks and Heterogeneous Media, 2007, 2(3): 397-423. doi: 10.3934/nhm.2007.2.397
[2]	Debora Amadori, Stefania Ferrari, Luca Formaggia . Derivation and analysis of a fluid-dynamical model in thin and long elastic vessels. Networks and Heterogeneous Media, 2007, 2(1): 99-125. doi: 10.3934/nhm.2007.2.99
[3]	Grigory Panasenko, Ruxandra Stavre . Asymptotic analysis of a non-periodic flow in a thin channel with visco-elastic wall. Networks and Heterogeneous Media, 2008, 3(3): 651-673. doi: 10.3934/nhm.2008.3.651
[4]	Serge Nicaise, Cristina Pignotti . Asymptotic analysis of a simple model of fluid-structure interaction. Networks and Heterogeneous Media, 2008, 3(4): 787-813. doi: 10.3934/nhm.2008.3.787
[5]	Grigory Panasenko, Ruxandra Stavre . Asymptotic analysis of the Stokes flow with variable viscosity in a thin elastic channel. Networks and Heterogeneous Media, 2010, 5(4): 783-812. doi: 10.3934/nhm.2010.5.783
[6]	Gung-Min Gie, Makram Hamouda, Roger Temam . Asymptotic analysis of the Navier-Stokes equations in a curved domain with a non-characteristic boundary. Networks and Heterogeneous Media, 2012, 7(4): 741-766. doi: 10.3934/nhm.2012.7.741
[7]	S. E. Pastukhova . Asymptotic analysis in elasticity problems on thin periodic structures. Networks and Heterogeneous Media, 2009, 4(3): 577-604. doi: 10.3934/nhm.2009.4.577
[8]	Michael Eden, Michael Böhm . Homogenization of a poro-elasticity model coupled with diffusive transport and a first order reaction for concrete. Networks and Heterogeneous Media, 2014, 9(4): 599-615. doi: 10.3934/nhm.2014.9.599
[9]	V. V. Zhikov, S. E. Pastukhova . Korn inequalities on thin periodic structures. Networks and Heterogeneous Media, 2009, 4(1): 153-175. doi: 10.3934/nhm.2009.4.153
[10]	Gianni Dal Maso, Francesco Solombrino . Quasistatic evolution for Cam-Clay plasticity: The spatially homogeneous case. Networks and Heterogeneous Media, 2010, 5(1): 97-132. doi: 10.3934/nhm.2010.5.97

Abstract

References

[1]	R. Ziadi, A. Bencherif-Madani, A perturbed quasi-Newton algorithm for bound-constrained global optimization, J. Comput. Math., 43 (2025), 143–173. https://doi.org/10.4208/jcm.2307-m2023-0016 doi: 10.4208/jcm.2307-m2023-0016
[2]	R. Ziadi, A. Bencherif-Madani, A mixed algorithm for smooth global optimization, J. Math. Model., 11 (2023), 207–228. https://doi.org/10.22124/JMM.2022.23133.2061 doi: 10.22124/JMM.2022.23133.2061
[3]	O. O. O. Yousif, R. Ziadi, M. A. Saleh, A. Z. Almaymuni, Another updated parameter for the Hestenes-Stiefel conjugate gradient method, Int. J. Anal. Appl., 23 (2025), 10. https://doi.org/10.28924/2291-8639-23-2025-10 doi: 10.28924/2291-8639-23-2025-10
[4]	C. Souli, R. Ziadi, A. Bencherif-Madani, H. M. Khudhur, A hybrid CG algorithm for nonlinear unconstrained optimization with application in image restoration, J. Math. Model., 12 (2024), 301–317. https://doi.org/10.22124/JMM.2024.26151.2317 doi: 10.22124/JMM.2024.26151.2317
[5]	Y. Chen, H. Huang, K. Huang, M. Roohi, C. Tang, A selective chaos-driven encryption technique for protecting medical images, Phys. Scr., 100 (2025), 0152a3. https://doi.org/10.1088/1402-4896/ad9fad doi: 10.1088/1402-4896/ad9fad
[6]	K. Xiong, S. Wang, The online random Fourier features conjugate gradient algorithm, IEEE Signal Process. Lett., 26 (2019), 740–744. https://doi.org/10.1109/LSP.2019.2907480 doi: 10.1109/LSP.2019.2907480
[7]	M. A. Saleh, Enhancing deep learning optimizers for detecting malware using line search method under strong Wolfe conditions, in 2023 3rd International Conference on Computing and Information Technology (ICCIT), (2023), 222–226. https://doi.org/10.1109/ICCIT58132.2023.10273908
[8]	M. Zhang, X. Wang, X. Chen, A. Zhang, The kernel conjugate gradient algorithms, IEEE Trans. Signal Process., 66 (2018), 4377–4387. https://doi.org/10.1109/TSP.2018.2853109 doi: 10.1109/TSP.2018.2853109
[9]	K. Xiong, H. H. Lu, S. Wang, Kernel correntropy conjugate gradient algorithms based on half-quadratic optimization, IEEE Trans. Cyber., 55 (2020), 5497–5510. https://doi.org/10.1109/TCYB.2019.2959834 doi: 10.1109/TCYB.2019.2959834
[10]	R. Ziadi, R. Ellaia, A. Bencherif-Madani, Global optimization through a stochastic perturbation of the PolakC Ribière conjugate gradient method, J. Comput. Appl. Math., 317 (2017), 672–684. https://doi.org/10.1016/j.cam.2016.12.021 doi: 10.1016/j.cam.2016.12.021
[11]	A. Mehamdia, Y. Chaib, T. Bechouat, Two modified conjugate gradient methods for unconstrained optimization and applications, RAIRO Oper. Res., 57 (2023), 333–353. https://doi.org/10.1051/ro/2023010 doi: 10.1051/ro/2023010
[12]	M. R. Hestenes, E. Stiefel, Methods of conjugate gradients for solving linear systems, J. Res. Natl. Bur. Stand., 49 (1952), 409–436.
[13]	R. Fletcher, Practical Methods of Optimization, Wiley, New York, 1997.
[14]	B. T. Polyak, The conjugate gradient method in extreme problems, USSR Comput. Math. Math. Phys., 9 (1969), 94–112. https://doi.org/10.1016/0041-5553(69)90035-4 doi: 10.1016/0041-5553(69)90035-4
[15]	E. Polak, G. Ribiere, Note sur la convergence de méthodes de directions conjuguées, Rev. Française Inf. Rech. Opr., 16 (1969), 35–43.
[16]	Y. Liu, C. Storey, Efficient generalized conjugate gradient algorithms. Part 1: Theory, J. Optim. Theory Appl., 69 (1992), 129–137. https://doi.org/10.1007/BF00940464 doi: 10.1007/BF00940464
[17]	Y. H. Dai, Y. Yuan, An efficient hybrid conjugate gradient method for unconstrained optimization, Ann. Oper. Res., 103 (2001), 33–47. https://doi.org/10.1023/A:1012930416777 doi: 10.1023/A:1012930416777
[18]	D. Ahmed, C. Storey, Efficient hybrid conjugate gradient techniques, J. Optim. Theory Appl., 64 (1990), 379–397. https://doi.org/10.1007/BF00939455 doi: 10.1007/BF00939455
[19]	J. K. Liu, S. J. Li, New hybrid conjugate gradient method for unconstrained optimization, Appl. Math. Comput., 245 (2014), 36–43. https://doi.org/10.1016/j.amc.2014.07.096 doi: 10.1016/j.amc.2014.07.096
[20]	N. Andrei, Another nonlinear conjugate gradient algorithm for unconstrained optimization, Optim. Meth. Soft., 24 (2008), 89–104. https://doi.org/10.1080/10556780802393326 doi: 10.1080/10556780802393326
[21]	X. Y. Zheng, X. L. Dong, J. R. Shi, W. Yang, Further comment on another hybrid conjugate gradient algorithm for unconstrained optimization by Andrei, Numer. Algorithms, 84 (2019), 603–608. https://doi.org/10.1007/s11075-019-00771-1 doi: 10.1007/s11075-019-00771-1
[22]	S. S. Djordjevic New hybrid conjugate gradient method as a convex combination of LS and CD methods, Filomat, 31 (2017), 1813–1825. https://doi.org/10.1007/s10473-019-0117-6 doi: 10.1007/s10473-019-0117-6
[23]	C. Souli, R. Ziadi, I. E. Lakhdari, A. Leulmi, An efficient hybrid conjugate gradient method for unconstrained optimization and image restoration problems, Iran. J. Numer. Anal. Optim., 15 (2024), 99–123. https://doi.org/10.1109/LSP.2019.290748010.22067/ijnao.2024.88087.1449 doi: 10.1109/LSP.2019.290748010.22067/ijnao.2024.88087.1449
[24]	M. Rivaie, M. Mamat, L. W. June, I. Mohd, A new class of nonlinear conjugate gradient coefficients with global convergence properties, Appl. Math. Comput., 218 (2012), 11323–11332. https://doi.org/10.1016/j.amc.2012.05.030 doi: 10.1016/j.amc.2012.05.030
[25]	Z. X. Wei, S. W. Yao, L. Y. Liu, The convergence properties of some new conjugate gradient methods, Appl. Math. Comput., 183 (2006), 1341–1350. https://doi.org/10.1016/j.amc.2006.05.150 doi: 10.1016/j.amc.2006.05.150
[26]	L. Zhang, An improved Wei-Yao-Liu nonlinear conjugate gradient method for optimization computation, J. Appl. Math. Comput., 215 (2009), 2269–2274. https://doi.org/10.1016/j.amc.2009.08.016 doi: 10.1016/j.amc.2009.08.016
[27]	I. M. Sulaiman, N. A. Bakar, M. Mamat, B. A. Hassan, M. Malik, M. A. Ahmed, A new hybrid conjugate gradient algorithm for optimization models and its application to regression analysis, J. Electr. Eng. Comput. Sci., 23 (2021), 1100–1109. https://doi.org/10.11591/ijeecs.v23.i2.pp1100-1109 doi: 10.11591/ijeecs.v23.i2.pp1100-1109
[28]	S. Yao, Z. Wei, H. Huang, A note about WYLs conjugate gradient method and its applications, Appl. Math. Comput., 191 (2007), 381–388. https://doi.org/10.1016/j.amc.2007.02.094 doi: 10.1016/j.amc.2007.02.094
[29]	I. Bongartz, A. R. Conn, N. Gould, P. L. Toint, CUTEr: A constrained and unconstrained testing environment, ACM Trans. Math. Softw. 29 (2003), 373–394. https://doi.org/10.1145/962437.96243 doi: 10.1145/962437.96243
[30]	N. Andrei, An unconstrained optimization test functions, Adv. Mode. Optim., 10 (2008), 147–161.
[31]	M. Hamoda, M. Mamat, M. Rivaie, Z. Salleh, A conjugate gradient method with strong Wolfe-Powell line search for unconstrained optimization, Appl. Math. Sci., 10 (2016), 13–16. http://dx.doi.org/10.12988/ams.2016.56449 doi: 10.12988/ams.2016.56449
[32]	I. E. Livieris, P. Pintelas, Globally convergent modified Perrys conjugate gradient method, Appl. Math. Comput., 218 (2012), 9197–9207. https://doi.org/10.1016/j.amc.2012.02.076 doi: 10.1016/j.amc.2012.02.076
[33]	W. W. Hager, H. Zhang, A new conjugate gradient method with guaranteed descent and an efficient line search, SIAM J. Optim., 16 (2005), 170–192. https://doi.org/10.1137/030601880 doi: 10.1137/030601880
[34]	E. D. Dolan, J. J. Mor, Benchmarking optimization software with performance profiles, Math. Program., 91 (2002), 201–213. https://doi.org/10.1007/s101070100263 doi: 10.1007/s101070100263

This article has been cited by:

1.	M. Bukač, S. Čanić, B. Muha, A partitioned scheme for fluid–composite structure interaction problems, 2015, 281, 00219991, 493, 10.1016/j.jcp.2014.10.045
2.	Liquan Wang, Jianguo Qin, Flow Curve Optimization Design for Offshore Backfilling Plough Fenders, 2018, 82, 0749-0208, 263, 10.2112/SI82-038.1
3.	Vishal Anand, Ivan C. Christov, Revisiting steady viscous flow of a generalized Newtonian fluid through a slender elastic tube using shell theory, 2021, 101, 0044-2267, 10.1002/zamm.201900309
4.	Charles Puelz, Sunčica Čanić, Béatrice Rivière, Craig G. Rusin, Comparison of reduced models for blood flow using Runge–Kutta discontinuous Galerkin methods, 2017, 115, 01689274, 114, 10.1016/j.apnum.2017.01.005
5.	Abdallah Daddi-Moussa-Ider, Maciej Lisicki, Stephan Gekle, Hydrodynamic mobility of a sphere moving on the centerline of an elastic tube, 2017, 29, 1070-6631, 111901, 10.1063/1.5002192
6.	Charles Puelz, Sebastián Acosta, Béatrice Rivière, Daniel J. Penny, Ken M. Brady, Craig G. Rusin, A computational study of the Fontan circulation with fenestration or hepatic vein exclusion, 2017, 89, 00104825, 405, 10.1016/j.compbiomed.2017.08.024
7.	M. Bukač, S. Čanić, R. Glowinski, B. Muha, A. Quaini, A modular, operator-splitting scheme for fluid-structure interaction problems with thick structures, 2014, 74, 02712091, 577, 10.1002/fld.3863
8.	Vishal Anand, Ivan C. Christov, Transient compressible flow in a compliant viscoelastic tube, 2020, 32, 1070-6631, 112014, 10.1063/5.0022406
9.	Giovanna Guidoboni, Roland Glowinski, Nicola Cavallini, Suncica Canic, Sergey Lapin, A kinematically coupled time-splitting scheme for fluid–structure interaction in blood flow, 2009, 22, 08939659, 684, 10.1016/j.aml.2008.05.006
10.	Paola Causin, Francesca Malgaroli, Mathematical modeling of local perfusion in large distensible microvascular networks, 2017, 323, 00457825, 303, 10.1016/j.cma.2017.05.015
11.	N. K. C. Selvarasu, Danesh K. Tafti, Investigation of the Effects of Dynamic Change in Curvature and Torsion on Pulsatile Flow in a Helical Tube, 2012, 134, 0148-0731, 10.1115/1.4006984
12.	Mario Bukal, Boris Muha, 2021, Chapter 8, 978-3-030-68143-2, 203, 10.1007/978-3-030-68144-9_8
13.	G.P. Panasenko, R. Stavre, Viscous fluid-thin cylindrical elastic layer interaction: asymptotic analysis, 2014, 93, 0003-6811, 2032, 10.1080/00036811.2014.911843
14.	Mario Bukal, Boris Muha, Justification of a nonlinear sixth-order thin-film equation as the reduced model for a fluid–structure interaction problem, 2022, 35, 0951-7715, 4695, 10.1088/1361-6544/ac7d89
15.	Martina Bukač, Sunčica Čanić, Josip Tambača, Yifan Wang, Fluid–structure interaction between pulsatile blood flow and a curved stented coronary artery on a beating heart: A four stent computational study, 2019, 350, 00457825, 679, 10.1016/j.cma.2019.03.034
16.	G. P. Panasenko, R. Stavre, Three Dimensional Asymptotic Analysis of an Axisymmetric Flow in a Thin Tube with Thin Stiff Elastic Wall, 2020, 22, 1422-6928, 10.1007/s00021-020-0484-8
17.	Mario Bukal, Boris Muha, Rigorous Derivation of a Linear Sixth-Order Thin-Film Equation as a Reduced Model for Thin Fluid–Thin Structure Interaction Problems, 2021, 84, 0095-4616, 2245, 10.1007/s00245-020-09709-9
18.	Sebastián Acosta, Charles Puelz, Béatrice Rivière, Daniel J. Penny, Ken M. Brady, Craig G. Rusin, Cardiovascular mechanics in the early stages of pulmonary hypertension: a computational study, 2017, 16, 1617-7959, 2093, 10.1007/s10237-017-0940-4
19.	G. P. Panasenko, R. Stavre, Viscous Fluid–Thin Elastic Plate Interaction: Asymptotic Analysis with Respect to the Rigidity and Density of the Plate, 2020, 81, 0095-4616, 141, 10.1007/s00245-018-9480-2
20.	Irina Malakhova-Ziablova, Grigory Panasenko, Ruxandra Stavre, Asymptotic analysis of a thin rigid stratified elastic plate – viscous fluid interaction problem, 2016, 95, 0003-6811, 1467, 10.1080/00036811.2015.1132311
21.	G. P. Panasenko, R. Stavre, Viscous fluid-thin cylindrical elastic body interaction: asymptotic analysis on contrasting properties, 2019, 98, 0003-6811, 162, 10.1080/00036811.2018.1442000
22.	Charles Puelz, Béatrice Rivière, A priori error estimates of Adams-Bashforth discontinuous Galerkin Methods for scalar nonlinear conservation laws, 2018, 26, 1570-2820, 151, 10.1515/jnma-2017-0011
23.	Abdallah Daddi-Moussa-Ider, Maciej Lisicki, Stephan Gekle, Slow rotation of a spherical particle inside an elastic tube, 2018, 229, 0001-5970, 149, 10.1007/s00707-017-1965-6
24.	Giovanna Guidoboni, Alon Harris, Lucia Carichino, Yoel Arieli, Brent A. Siesky, Effect of intraocular pressure on the hemodynamics of the central retinal artery: A mathematical model, 2014, 11, 1551-0018, 523, 10.3934/mbe.2014.11.523
25.	G. P. Panasenko, R. Stavre, Asymptotic analysis of a viscous fluid–thin plate interaction: Periodic flow, 2014, 24, 0218-2025, 1781, 10.1142/S0218202514500079
26.	Sophie Marbach, Noah Ziethen, Karen Alim, Vascular adaptation model from force balance: Physarum polycephalum as a case study, 2023, 25, 1367-2630, 123052, 10.1088/1367-2630/ad1488
27.	Jeffrey Kuan, Sunčica Čanić, Boris Muha, Existence of a weak solution to a regularized moving boundary fluid-structure interaction problem with poroelastic media, 2024, 351, 1873-7234, 505, 10.5802/crmeca.190
28.	Kristina Kaulakytė, Nikolajus Kozulinas, Grigory Panasenko, Konstantinas Pileckas, Vytenis Šumskas, Poiseuille-Type Approximations for Axisymmetric Flow in a Thin Tube with Thin Stiff Elastic Wall, 2023, 11, 2227-7390, 2106, 10.3390/math11092106
29.	Laura Miller, Salvatore Di Stefano, Alfio Grillo, Raimondo Penta, Homogenised governing equations for pre-stressed poroelastic composites, 2023, 35, 0935-1175, 2275, 10.1007/s00161-023-01247-3
30.	Maxime Krier, Julia Orlik, Grigory Panasenko, Konrad Steiner, Asymptotically Proved Numerical Coupling of a 2D Flexural Porous Plate with the 3D Stokes Fluid, 2024, 22, 1540-3459, 1608, 10.1137/23M1627687
31.	Maxime Krier, Julia Orlik, René Pinnau, Multi-scale optimization problem for the flow-induced displacement of a periodic filter medium, 2025, 1389-4420, 10.1007/s11081-025-09979-8

Reader Comments

Your name:*

Email:*
© 2025 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)