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Global convergence property with inexact line search for a new conjugate gradient method

[19] Hamel, N., Benrabia, N., Ghiat, M., & Gueb- [30] Djordjevi´c, S. S. (2016). New hybrid conjugate
bai, H. (2024). Developing a new conjugate gradi- gradient method as a convex combination of FR
ent algorithm with the bebefit of some desirable and PRP methods. Filomat, 30(11), 3083-3100.
properties of the newton algorithm for uncon- https://doi.org/10.2298/FIL1611083D
strained optimization. Journal of Applied Anal- [31] Hamdi, H., Sellami, B., & Bellofi, M. (2020). A
ysis and Computation, 14(1), 458-472. https: new hybrid conjugate gradient method as a con-
//doi.org/10.11948/20230268 vex combination of DY and BA methods. Com-
[20] Hallal, A., Belloufi, M., & Sellami, B. (2024). A munications in Optimization Theory, 2020, 1-9.
new hybrid CG method as convex combination. [32] Andrei, N. (2008). An unconstrained optimization
Mathematical Foundations of Computing, 7(4), test functions collection. Advanced Modeling and
522-530. https://doi.org/10.3934/mfc.20 Optimization, 10, 147-161.
23028 [33] Dolan, E. D., & Mor´e, J. J. (2002). Benchmarking
[21] Guefassa, I., Chaib, Y., & Bechouat, T. (2023). A optimization software with performance profiles.
hybrid conjugate gradient method between MLS Mathematical Programming, 91, 201-213. https:
and FR in nonparametric statistics. Communica- //doi.org/10.1007/s101070100263
tions in Combinatorics and Optimization. [34] Dai, Y. H., & Yuan, Y. (2001). An efficient hybrid
[22] Delladji, S., Belloufi, M., & Sellami, B. (2021). conjugate gradient method for unconstrained op-
Behavior of the combination of PRP and HZ timization. Annals of Operations Research, 103,
methods for unconstrained optimization. Numer- 33-47. https://doi.org/10.1023/A:10129304
ical Algebra, Control and Optimization, 11(3), 16777
377-389. https://doi.org/10.3934/naco.2 [35] Hanachi, S. B., Sellami, B., & Belloufi, M. (2022).
020032 New iterative conjugate gradient method for
[23] Delladji, S., Belloufi, M., & Sellami, B. (2021). nonlinear unconstrained optimization. RAIRO-
New hybrid conjugate gradient method as a con- Operations Research, 56(4), 2315-2327. https:
vex combination of FR and BA methods. Journal //doi.org/10.1051/ro/2022109
of Information and Optimization Sciences, 42(3), [36] Chaib, Y., & Bechouat, T. (2023). Two modified
591-602. https://doi.org/10.1080/02522667 conjugate gradient methods for solving uncon-
.2020.1778841 strained optimization and application. RAIRO-
[24] Djordjevi´c, S. S. (2018). New hybrid conjugate Operations Research, 57(2), 333-350. https://
gradient method as a convex combination of HS doi.org/10.1051/ro/2023010
and FR conjugate gradient methods. Journal of
Applied Mathematics and Computation, 2, 366-
378. https://doi.org/10.26855/jamc.2018.0
9.002 Sabrina Ben Hanachi is a Ph.D. student at Mo-
[25] Al-Bayati, A. Y., & Al-Assady, N. H. (1986). hamed Cherif Messaadia University, Algeria, since
Conjugate gradient method. Technical Research. 2022, specializing in nonlinear optimization. She has
School of Computer Studies, Leeds University, also published two articles in the RAIRO-Operations
UK. Research journal, the first in 2022 and the second in
[26] Hager, W. W., & Zhang, H. (2005). A new con- 2024. Her research interests include numerical analy-
jugate gradient method with guaranteed descent sis and applied mathematics. https://orcid.or
and an efficient line search. Society for Industrial g/0000-0003-3610-3346
and Applied Mathematics Journal on Optimiza-
tion, 16(1), 170-192. https://doi.org/10.113
Badreddine Sellami is a professor in the Depart-
7/030601880
ment of Mathematics and Computer Science at Mo-
[27] Andrei, N. (2009). New hybrid conjugate gradient
hammed Cherif Messaadia University in Souk-Ahras,
algorithms for unconstrained optimization. Ad-
Algeria. He received his Ph.D. in Functional Analysis
vanced Modeling and Optimization, 8-10.
and Optimization from Badji-Mokhtar University, Al-
[28] Bongartz, I., Conn, A. R., Gould, N., & Toint,
geria, in 2014. His research primarily focuses on the
P. L. (1995). CUTE: constrained and uncon-
application of mathematical methods to optimization
strained testing environments. ACM Transactions
problems.
on Mathematical Software (TOMS), 21(1), 123-
https://orcid.org/0009-0007-6981-5207
160. https://doi.org/10.1145/200979.20104
3
[29] Delladji, S., Belloufi, M., & Sellami, B. (2021). Mohammed Belloufi is a professor at the Depart-
New hybrid conjugate gradient method as a con- ment of Mathematics and Computer Science at Mo-
vex combination of FR and BA methods. Journal hammed Cherif Messaadia University in Souk-Ahras,
of Information and Optimization Sciences, 42(3), Algeria. He received his Ph.D in Numerical Analysis
p. 591-602. https://doi.org/10.1080/025226 and Optimization from Badji-Mokhtar University, Al-
67.2020.1778841 geria in 2014.
https://orcid.org/0000-0001-7877-0230

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