Open Access
Issue
RAIRO-Oper. Res.
Volume 59, Number 5, September-October 2025
Page(s) 2437 - 2449
DOI https://doi.org/10.1051/ro/2025106
Published online 05 September 2025
  • M. Abdullahi, A.S. Halilu, A.M. Awwal and N. Pakkaranang, On efficient matrix-free method via quasi-Newton approach for solving system of nonlinear equations. Adv. Theory Nonlinear Anal. Appl. 5 (2021) 568–579. [Google Scholar]
  • A.B. Abubakar, P. Kumam, J.K. Liu, H. Mohammad and C. Tammer, New three-term conjugate gradient algorithm for solving monotone nonlinear equations and signal recovery problems. Int. J. Comput. Math. 100 (2023) 1992–2013. [Google Scholar]
  • K. Ahmed, M.Y. Waziri, S. Murtala, A.S. Halilu and J. Sabi’u, On a scaled symmetric Dai–Liao-Type scheme for constrained system of nonlinear equations with applications. J. Optim. Theory Appl. 200 (2024) 669–702. [Google Scholar]
  • N. Andrei, An accelerated subspace minimization three-term conjugate gradient algorithm for unconstrained optimization. Numer. Algorithms 65 (2014) 859–874. [CrossRef] [MathSciNet] [Google Scholar]
  • I. Bongartz, A.R. Conn, N. Gould and P.L. Toint, CUTEr: constrained and unconstrained testing enviroment. ACM Trans. Math. Softw. 21 (1995) 123–160. [CrossRef] [Google Scholar]
  • S.P. Dirkse and M.C. Ferris, MCPLIB: a collection of nonlinear mixed complementarity problems. Optim. Methods Softw. 5 (1995) 319–345. [Google Scholar]
  • E.D. Dolan and J.J. Moré, Benchmarking optimization software with performance profiles. Math. Prog. 91 (2002) 201–213. [CrossRef] [Google Scholar]
  • A.H. Ibrahim and S. Al-Homidan, Two-step inertial derivative-free projection method for solving nonlinear equations with application. J. Comput. Appl. Math. 451 (2024) 116071. [Google Scholar]
  • A.H. Ibrahim and S. Al-Homidan, A derivative-free projection method with double inertial effects for solving non-linear equations. Appl. Numer. Math. 209 (2025) 55–67. [Google Scholar]
  • A.H. Ibrahim, M. Alshahrani and S. Al-Homidan, Two classes of spectral three-term derivative-free method for solving nonlinear equations with application. Numer. Algorithm 96 (2024) 1625–1645. [Google Scholar]
  • A.H. Ibrahim, S. Rapajić, A. Kamandi, P. Kumam and Z. Papp, Relaxed-inertial derivative-free algorithm for systems of nonlinear pseudo-monotone equations. Comput. Appl. Math. 43 (2024) 239. [Google Scholar]
  • J.B. Jian, J.C. Jin and G.D. Ma, An IDFPM-based algorithm without Lipschitz continuity to constrained nonlinear equations for sparse signal and blurred image restoration problems. J. Comput. Appl. Math. 456 (2025) 116234. [Google Scholar]
  • Q. Li, G.L. Chen and M.L. Liang, An efficient spectral three-term derivative-free projection algorithm for a large-scale system of monotone nonlinear equations. Comput. Appl. Math. 44 (2025) 160. [Google Scholar]
  • D.D. Li, Y. Li, Y.F. Li and S.H. Wang, A modified PRP-type derivative-free projection algorithm for constrained nonlinear equations with applications. Comput. Appl. Math. 44 (2025) 48. [Google Scholar]
  • H.W. Liu and Z.X. Liu, An efficient Barzilai-Borwein conjugate gradient method for unconstrained optimization. J. Optim. Theory Appl. 180 (2019) 879–906. [CrossRef] [MathSciNet] [Google Scholar]
  • J.K. Liu, Z.L. Lu and J.L. Xu, An efficient projection-based algorithm without Lipschitz continuity for large-scale nonlinear pseudo-monotone equations. J. Comput. Appl. Math. 403 (2022) 113822. [CrossRef] [Google Scholar]
  • J.K. Liu, B. Tang, T. Liu, Z.T. Yang and S. Liang, An accelerated double-step derivative-free projection method based algorithm using Picard–Mann iterative process for solving convex constrained nonlinear equations. J. Comput. Appl. Math. 464 (2025) 116541. [Google Scholar]
  • J.K. Liu, B. Tang, N. Zhang, J. Xiong, P. T. Gao and X. L. Dong, A subspace derivative-free projection method for convex constrained nonlinear equations. Jpn. J. Ind. Appl. Math. 42 (2025) 197–221. [Google Scholar]
  • J.K. Liu, N. Zhang, B. Tang, J. Xiong and Y.M. Feng, An accelerated derivative-free method for solving large-scale nonlinear non-monotone equations. Optimization (2025) 1–24. [Google Scholar]
  • G.D. Ma, J.C. Jin, J.B. Jian, J.H. Yin and D.H. Han, A modified inertial three-term conjugate gradient projection method for constrained nonlinear equations with applications in compressed sensing. Numer. Algorithms 92 (2023) 1621–1653. [Google Scholar]
  • J. Sabi’u and R.Z. Al-Kawaz, An efficient modified conjugate gradient parameter for solving the system of symmetric nonlinear equations with application in motion control of coplanar robot. Comput. Appl. Math. 44 (2025) 49. [Google Scholar]
  • T.Y. Song and Z.X. Liu, An efficient inertial subspace minimization CG algorithm with convergence rate analysis for constrained nonlinear monotone equations. J. Comput. Appl. Math. 446 (2024) 115873. [Google Scholar]
  • T.Y. Song and Z.X. Liu, An efficient subspace minimization conjugate gradient method for solving nonlinear monotone equations with convex constraints. Axioms 13 (2024) 170. [Google Scholar]
  • W. Sun, H. Liu and Z.X. Liu, A class of accelerated subspace minimization conjugate gradient methods. J. Optim. Theory Appl. 190 (2021) 811–840. [Google Scholar]
  • M.W. Yusuf, L. June and M.A. Hassan, Jacobian-free diagonal Newton’s method for solving nonlinear systems with singular Jacobian. Malays. J. Math. Sci. 5 (2011) 241–255. [Google Scholar]
  • J.H. Yin, J.B. Jian, X.Z. Jiang and X.D. Wu, A family of inertial-relaxed DFPM-based algorithms for solving large-scale monotone nonlinear equations with application to sparse signal restoration. J. Comput. Appl. Math. 419 (2023) 114674. [Google Scholar]
  • J.H. Yin, J.B. Jian and G.D. Ma, A modified inexact Levenberg–Marquardt method with the descent property for solving nonlinear equations. Comput. Optim. Appl. 87 (2024) 289–322. [Google Scholar]
  • Y.-X. Yuan and J. Stoer, A subspace study on conjugate gradient algorithms. Z. Angew. Math. Mech. 75 (1995) 69–77. [CrossRef] [MathSciNet] [Google Scholar]
  • G.L. Yuan and M.J. Zhang, A three-terms Polak–Ribiére–Polyak conjugate gradient algorithm for large-scale non-linear equations. J. Comput. Appl. Math. 286 (2015) 186–195. [CrossRef] [MathSciNet] [Google Scholar]
  • K.K. Zhang, H.W. Liu and Z.X. Liu, A new adaptive subspace minimization three-term conjugate gradient algorithm for unconstrained optimization. J. Comput. Math. 39 (2021) 159–177. [Google Scholar]
  • N. Zhang, J.K. Liu and B. Tang, A three-term projection method based on spectral secant equation for nonlinear monotone equations. Jpn. J. Ind. Appl. Math. 41 (2024) 617–635. [Google Scholar]
  • Y. Zhao, M.J. Niu and J.K. Liu, A three-term subspace projection method for solving systems of nonlinear monotone equations. J. Ind. Manage. Optim. 21 (2024) 1931–1945. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.