[1] Z. Aminifard, S. Babaie-Kafaki, Dai-Liao extensions of a descent hybrid nonlinear conjugate gra-
dient method with application in signal processing, Numer. Algorithms 89 (2021) 1369–1387.
[2] Z. Aminifard, S. Babaie-Kafaki, S. Ghafoori, An augmented memoryless BFGS method based on a
modified secant equation with application to compressed sensing, Appl. Numer. Math. 167 (2021)
187–201.
[3] N. Andrei, Eigenvalues versus singular values study in conjugate gradient algorithms for large-
scale unconstrained optimization, Optim. Methods Softw. 32 (2017) 534–551.
[4] N. Andrei, Diagonal Approximation of the Hessian by Finite Differences for Unconstrained Opti-
mization, J. Optim. Theory Appl. 185 (2020) 859–879.
[5] N. Andrei, New conjugate gradient algorithms based on self-scaling memoryless Broyden-Fletcher-
Goldfarb-Shanno method, Calcolo 57 (2020) 1–27.
[6] N. Andrei, A double parameter self-scaling memoryless BFGS method for unconstrained optimiza-
tion, Comput. Appl. Math. 39 (2020) 159.
[7] M.R. Arazm, S. Babaie-Kafaki, R. Ghanbari, An extended Dai-Liao conjugate gradient method
with global convergence for nonconvex functions, Matematicki 52 (2017) 361–375.
[8] S. Babaie-Kafaki, A modified scaled memoryless BFGS preconditioned conjugate gradient method
for unconstrained optimization, 4OR 11 (2013) 361–374.
[9] S. Babaie Kafaki, A modified scaling parameter for the memoryless BFGS updating formula, Nu-
mer. Algorithms 72 (2016) 425–433.
[10] S. Babaie-Kafaki, Z. Aminifard, Two parameter scaled memoryless BFGS methods with a non-
monotone choice for the initial step length, Numer. Algorithms 82 (2019) 1345–1357.
[11] S. Babaie-Kafaki, Z. Aminifard, S. Ghafoori, A hybrid quasi-Newton method with application in
sparse recovery, Comput. Appl. Math. 41 (2022) 249.
[12] S. Babaie-Kafaki, N. Mirhoseini, Z. Aminifard, A descent extension of a modified Polak–Ribire–
Polyak method with application in image restoration problem, Optim. Lett. 17 (2023) 351–367.
[13] C.G. Broyden, A class of methods for solving nonlinear simultaneous equations, Math. Comput. 19
(1965) 577–593.
[14] C.G. Broyden, The convergence of a class of double-rank minimization algorithms: 2. the new
algorithm, IMA J. Appl. Math. 6 (1970) 222–231.
[15] R.H. Byrd, J. Nocedal, A tool for the analysis of quasi-Newton methods with application to uncon-
strained minimization, SIAM J. Numer. Anal. 26 (1989) 727–739.
[16] R.H. Byrd, J. Nocedal, Y.-X. Yuan, Global convergence of a class of Quasi-Newton methods on
convex problems, SIAM J. Numer. Anal. 24 (1987) 1171–1190.
[17] Y. H. Dai, C.-X. Kou, A nonlinear conjugate gradient algorithm with an optimal property and an
improved Wolfe line search, SIAM J. Optim. 23 (2013) 296–320.
[18] J.E. Dennis, J.J. More, A characterization of superlinear convergence and its application to quasi-
Newton methods, Math. Comput. 28 (1974) 549–560.
[19] J.E. Dennis, J.J. More, Quasi-Newton methods, motivation and theory, SIAM Review 19 (1977)
46–89.
[20] J.E. Dennis, H. Wolkowicz, Sizing and least-change secant methods, SIAM J. Numer. Anal. 30
(1993).
[21] E.D. Dolan , J.J. More, Benchmarking optimization software with performance profiles, Math. Pro-
gram. 91 (2002) 201–213.
[22] L. Exl, J. Fischbacher, H. Oezelt, M. Gusenbauer, T. Schrefl, Preconditioned nonlinear conjugate
gradient method for micromagnetic energy minimization, Comput. Phys Commun. 235 (2019) 179–
186.
[23] N.I. Gould, D. Orban, P.L. Toint, Cuter and sifdec: A constrained and unconstrained testing envi-
ronment, revisited, ACM Trans. Math. Softw. 29 (2003) 373–394.
[24] A. R. Heravi, G. Abed Hodtani, A New Correntropy-Based Conjugate Gradient Backpropagation
Algorithm for Improving Training in Neural Networks, IEEE Trans. Neural Netw. Learn. Syst. 29
(2018) 6252–6263.
[25] D. H. Li, M. Fukushima, A modified BFGS method and its global convergence in nonconvex mini-
mization, J. Comput. Appl. Math. 129 (2001) 15–35.
[26] M. Li, H. Liu, Z. Liu, A new family of conjugate gradient methods for unconstrained optimization,
J. Appl. Math. Comput. 58 (2018) 219–234.
[27] W. Li, Y. Liu, J. Yang, W. Wu, A new conjugate gradient method with smoothing L1/2 regularization
based on a modified secant equation for training neural networks, Neural Process. Lett. 48 (2018)
955–978.
[28] A. Liao, Modifying the BFGS method, Oper. Res. Lett. 20 (1997) 171–177.
[29] J. Lin, C. Jiang, An improved conjugate gradient parametric detection based on space-time scan,
Signal Process. 169 (2020) 107412.
[30] I.E. Livieris, V. Tampakas, P. Pintelas, A descent hybrid conjugate gradient method based on the
memoryless BFGS update, Numer. Algorithms 79 (2018) 1169–1185.
[31] S. Nezhadhossein, New nonlinear conjugate gradient methods based on optimal Dai-Liao param-
eters, J. Math. Model. 8 (2020) 21–39.
[32] S. Nezhadhossein, A modified descent spectral conjugate gradient method for unconstrained opti-
mization, Iran. J. Sci. Technol. Trans. A Sci. 45 (2021) 209–220.
[33] J. Nocedal, S. J. Wright, Numerical Optimization, Springer Series in Operations Research.
Springer-Verlag, New York, 1999.
[34] S.S. Oren, D.G. Luenberger, Self-scaling variable metric (ssvm) algorithms: Part i: Criteria and
sufficient conditions for scaling a class of algorithms, Manag. Sci. 20 (19774) 845–862.
[35] S.S. Oren, E. Spedicato, Optimal conditioning of self-scaling variable metric algorithms, Math.
Program. 10 (1976) 70–90.
[36] K. Sugiki, Y. Narushima, H. Yabe, Globally convergent three-term conjugate gradient methods
that use secant conditions and generate descent search directions for unconstrained optimization,
J. Optim. Theory Appl. 153 (2012) 733–757.
[37] W. Sun, Y.-X. Yuan, Optimization Theory and Methods: Nonlinear Programming, Springer, New
York, 2006.
[38] N. Ullah, J. Sabiu, A. Shah, A derivative-free scaling memoryless Broyden-Fletcher-Goldfarb-
Shanno method for solving a system of monotone nonlinear equations, Numer. Linear Algebra
Appl. 28 (2021) e2374.
[39] Z. Wei, G. Li, L. Qi, New quasi-Newton methods for unconstrained optimization problems, Appl.
Math. Comput. 175 (2006) 1156–1188.
[40] R. Winther, Some superlinear convergence results for the conjugate gradient method, SIAM J.
Numer. Anal. 17 (1980) 14–17.
[41] G. Yu, J. Huang, Y. Zhou, A descent spectral conjugate gradient method for impulse noise removal,
Appl. Math. Lett. 23 (2010) 555–560.
[42] G. Yuan, J. Lu, Z. Wang The PRP conjugate gradient algorithm with a modified WWP line search
and its application in the image restoration problems, Appl. Numer. Math. 152 (2020) 1–11.
[43] J.Z. Zhang, N.Y. Deng, L.H. Chen, New quasi-Newton equation and related methods for uncon-
strained optimization, J. Optim. Theory Appl. 102 (1999) 147–167.
[44] W. Zhou, L. Zhang, A nonlinear conjugate gradient method based on the MBFGS secant condition,
Optim. Methods Softw. 21 (2006) 707–714.
)