Free Access
Issue
RAIRO-Oper. Res.
Volume 54, Number 2, March-April 2020
Page(s) 489 - 505
DOI https://doi.org/10.1051/ro/2020008
Published online 02 March 2020
  • A.B. Abubakar and P. Kumam, An improved three-term derivative-free method for solving nonlinear equations. Comput. Appl. Math. 37 (2018) 6760–6773. [CrossRef] [Google Scholar]
  • A.B. Abubakar and P. Kumam, A descent Dai-Liao conjugate gradient method for nonlinear equations. Numer. Algorithms 81 (2019) 197–210. [Google Scholar]
  • A.B. Abubakar and M.Y. Waziri, A matrix-free approach for solving systems of nonlinear equations. J. Mod. Methods Numer. Math. 7 (2016) 1–9. [CrossRef] [Google Scholar]
  • A.B. Abubakar and P. Kumam, A.M. Awwal, P. Thounthong, A modified self-adaptive conjugate gradient method for solving convex constrained monotone nonlinear equations for signal reovery problems. Mathematics 7 (2019) 693. [CrossRef] [Google Scholar]
  • A.B. Abubakar, P. Kumam, H. Mohammad and A.M. Awwal, An efficient conjugate gradient method for convex constrained monotone nonlinear equations with applications. Mathematics 7 (2019) 767. [CrossRef] [Google Scholar]
  • A.B. Abubakar, P. Kumam, H. Mohammad, A.M. Awwal and S. Kanokwan, A modified Fletcher-Reeves conjugate gradient method for monotone nonlinear equations with some applications. Mathematics 7 (2019) 745. [CrossRef] [Google Scholar]
  • M. Ahookhosh, K. Amini and S. Bahrami, Two derivative-free projection approaches for systems of large-scale nonlinear monotone equations. Numer. Algorithms 64 (2013) 21–42. [Google Scholar]
  • J. Barzilai and J.M. Borwein, Two-point step size gradient methods. IMA J. Numer. Anal. 8 (1988) 141–148. [CrossRef] [MathSciNet] [Google Scholar]
  • S. Bellavia, D. Bertaccini and B. Morini, Nonsymmetric preconditioner updates in Newton–krylov methods for nonlinear systems. SIAM J. Sci. Comput. 33 (2011) 2595–2619. [Google Scholar]
  • Z. Dai, X. Chen and F. Wen, A modified Perry’s conjugate gradient method-based derivative-free method for solving large-scale nonlinear monotone equations. Appl. Math. Comput. 270 (2015) 378–386. [Google Scholar]
  • E.D. Dolanand J.J. Moré, Benchmarking optimization software with performance profiles. Math. Program. 91 (2002) 201–213. [Google Scholar]
  • P. Gao and C. He, An efficient three-term conjugate gradient method for nonlinear monotone equations with convex constraints. Calcolo 55 (2018) 53. [CrossRef] [Google Scholar]
  • B. Ghaddar, J. Marecek and M. Mevissen, Optimal power flow as a polynomial optimization problem. IEEE Trans. Power Syst. 31 (2016) 539–546. [Google Scholar]
  • Y. Hu and Z. Wei, Wei–Yao–Liu conjugate gradient projection algorithm for nonlinear monotone equations with convex constraints. Int. J. Comput. Math. 92 (2015) 2261–2272. [Google Scholar]
  • W. La Cruz and M. Raydan, Nonmonotone spectral methods for large-scale nonlinear systems. Optim. Methods Softw. 18 (2003) 583–599. [Google Scholar]
  • W. La Cruz, J. Martnez and M. Raydan, Spectral residual method without gradient information for solving large-scale nonlinear systems of equations. Math. Comput. 75 (2006) 1429–1448. [Google Scholar]
  • W.J. Leong, M.A. Hassan and M.Y. Waziri, A matrix-free quasi-Newton method for solving large-scale nonlinear systems. Comput. Math. App. 62 (2011) 2354–2363. [Google Scholar]
  • M. Li, An Liu-Storey-Type method for solving large-scale nonlinear monotone equations. Numer. Funct. Anal. Optim. 35 (2014) 310–322. [Google Scholar]
  • Q. Li and D.H. Li, A class of derivative-free methods for large-scale nonlinear monotone equations. IMA J. Numer. Anal. 31 (2011) 1625–1635. [CrossRef] [Google Scholar]
  • J. Liu and Y. Feng, A derivative-free iterative method for nonlinear monotone equations with convex constraints. Numer. Algorithms 82 (2018) 245–262. [Google Scholar]
  • J. Liu and S.J. Li, A projection method for convex constrained monotone nonlinear equations with applications. Comput. Math. App. 70 (2015) 2442–2453. [Google Scholar]
  • J.K. Liu and S.J. Li, A three-term derivative-free projection method for nonlinear monotone system of equations. Calcolo 53 (2016) 427–450. [CrossRef] [Google Scholar]
  • H. Liu, Z. Liu and X. Dong, A new adaptive Barzilai and Borwein method for unconstrained optimization. Optim. Lett. 12 (2018) 845–873. [Google Scholar]
  • F. Ma and C. Wang, Modified projection method for solving a system of monotone equations with convex constraints. J. Appl. Math. Comput. 34 (2010) 47–56. [Google Scholar]
  • H. Mohammad, Barzilai–Borwein-like method for solving large-scale non-linear systems of equations. J. Niger. Math. Soc. 36 (2017) 71–83. [Google Scholar]
  • H. Mohammad and A.B. Abubakar, A positive spectral gradient-like method for large-scale nonlinear monotone equations. Bull. Comput. Appl. Math. 5 (2017) 99–115. [Google Scholar]
  • H. Mohammad and M.Y. Waziri, On Broyden-like update via some quadratures for solving nonlinear systems of equations. Turkish J. Math. 39 (2015) 335–345. [CrossRef] [Google Scholar]
  • H. Mohammad and M.Y. Waziri, Structured two-point stepsize gradient methods for nonlinear least squares. J. Optim. Theory Appl. 181 (2019) 298–317. [Google Scholar]
  • J. Nocedal and S.J. Wright. Numerical Optimization. Springer Science (2006). [Google Scholar]
  • M. Raydan, On the Barzilai and Borwein choice of steplength for the gradient method. IMA J. Numer. Anal. 13 (1993) 321–326. [CrossRef] [Google Scholar]
  • M. Raydan, The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem. SIAM J. Optim. 7 (1997) 26–33. [Google Scholar]
  • M.V. Solodov and B.F. Svaiter, A globally convergent inexact Newton method for systems of monotone equations. Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods. Springer (1998) 355–369. [CrossRef] [Google Scholar]
  • W. Sun and Y.X. Yuan, Optimization Theory and Methods: Nonlinear Programming. Springer Science & Business Media 1 (2006). [Google Scholar]
  • C. Wang, Y. Wang and C. Xu, A projection method for a system of nonlinear monotone equations with convex constraints. Math. Methods Oper. Res. 66 (2007) 33–46. [CrossRef] [Google Scholar]
  • X.Y. Wang, S.J. Li and X.P. Kou, A self-adaptive three-term conjugate gradient method for monotone nonlinear equations with convex constraints. Calcolo 53 (2016) 133–145. [CrossRef] [Google Scholar]
  • M.Y. Waziri and J. Sabi’u, A derivative-free conjugate gradient method and its global convergence for solving symmetric nonlinear equations. Int. J. Math. Math. Sci. 2015 (2015) 961487. [Google Scholar]
  • M.Y. Waziri, W.J. Leong, M.A. Hassan and M. Monsi, Jacobian computation-free Newton’s method for systems of non-linear equations. J. Numer. Math. Stochastic 2 (2010) 54–63. [Google Scholar]
  • A.J. Wood and B.F. Wollenberg. Power Generation, Operation, and Control. John Wiley & Sons (2012). [Google Scholar]
  • Y. Xiao and H. Zhu, A conjugate gradient method to solve convex constrained monotone equations with applications in compressive sensing. J. Math. Anal. App. 405 (2013) 310–319. [CrossRef] [Google Scholar]
  • Q.R. Yan, X.Z. Peng and D.H. Li, A globally convergent derivative-free method for solving large-scale nonlinear monotone equations. J. Comput. Appl. Math. 234 (2010) 649–657. [Google Scholar]
  • Z. Yu, J. Lin, J. Sun, Y.H. Xiao, L. Liu and Z.H. Li, Spectral gradient projection method for monotone nonlinear equations with convex constraints. Appl. Numer. Math. 59 (2009) 2416–2423. [Google Scholar]
  • L. Zhang and W. Zhou, Spectral gradient projection method for solving nonlinear monotone equations. J. Comput. Appl. Math. 196 (2006) 478–484. [Google Scholar]
  • W.J. Zhou and D.H. Li, A globally convergent BFGS method for nonlinear monotone equations without any merit functions. Math. Comput. 77 (2008) 2231–2240. [Google Scholar]

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