Open Access
Issue
RAIRO-Oper. Res.
Volume 55, Number 6, November-December 2021
Page(s) 3293 - 3316
DOI https://doi.org/10.1051/ro/2021154
Published online 15 November 2021
  • Y. Bing and G. Lin, An Efficient Implementation of Merrill’s Method for Sparse or Partially Separable Systems of Nonlinear Equations. SIAM J. Optim. 1 (1991) 206–221. [Google Scholar]
  • S. Deng and Z. Wan, A diagonal quasi-newton spectral conjugate gradient algorithm for nonconvex unconstrained optimization problems. In: Proceedings of the 5th International Conference on Optimization and Control with Applications. Curtin University (2012) 305–310. [Google Scholar]
  • J.E. Dennis and J.J. Moré, A characterization of superlinear convergence and its application to quasi-Newton methods. Math. Comput. 28 (1974) 549–560. [Google Scholar]
  • E.D. Dolan and J.J. Moré, Benchmarking optimization software with performance profiles. Math. Program. 91 (2002) 201–213. [Google Scholar]
  • M.A. Gomes-Ruggiero, J.M. Martnez and A.C. Moretti, Comparing algorithms for solving sparse nonlinear systems of equations. SIAM J. Sci. Statist. Comput. 13 (1992) 459–483. [Google Scholar]
  • A. Griewank and PhL Toint, Local convergence analysis for partitioned quasi-newton updates. Numer. Math. 39 (1982) 429–448. [Google Scholar]
  • A. Griewank and Ph.L. Toint, On the unconstrained optimization of partially separable functions, in Nonlinear Optimization 1981., Academic press (1982) 301–312. [Google Scholar]
  • A. Griewank and PhL Toint, Partitioned variable metric updates for large structured optimization problems. Numer. Math. 39 (1982) 119–137. [Google Scholar]
  • C.T. Kelly, A comparison of iteration schemes for chandrasekhar h-equations in multigroup neutron transport. J. Math. Phys. 21 (1980) 408–409. [Google Scholar]
  • N. Krejiść, Z. Lužanin and I. Radeka, Newton-like method for nonlinear banded block diagonal system. Appl. Math. Comput. 189 (2007) 1705–1711. [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.M. Martnez and M. Raydan, Spectral residual method without gradient information for solving large-scale nonlinear systems: theory and experiments. Citeseer , Technical Report RT-04-08 (https://www.ime.unicamp.br/ martinez/lmrreport.pdf) (2004). [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.W. Yusuf, A matrix-free quasi-Newton method for solving large-scale nonlinear systems. Comput. Math. with Appl. 62 (2011) 2354–2363. [Google Scholar]
  • D. Li and M. Fukushima, A globally and superlinearly convergent Gauss–Newton-based BFGS method for symmetric nonlinear equations. SIAM J. Numer. Anal. 37 (1999) 152–172. [Google Scholar]
  • L. Lukšan, C. Matonoha and J. Vlcek, Problems for nonlinear least squares and nonlinear equations. Technical report (2018). [Google Scholar]
  • J.M. Martnez, Practical quasi-Newton methods for solving nonlinear systems. J. Comput. Appl. Math. 124 (2000) 97–121. [Google Scholar]
  • H. Mohammad, Barzilai-Borwein-like method for solving large-scale nonlinear systems of equations. J. Nigerian Math. Soc. 36 (2017) 71–83. [Google Scholar]
  • H. Mohammad and M.Y. Waziri, On Broyden-like update via some quadratures for solving nonlinear systems of equations. Turk. J. Math. 39 (2015) 335–345. [Google Scholar]
  • H. Mohammad and S.A. Santos, A structured diagonal Hessian approximation method with evaluation complexity analysis for nonlinear least squares. Comput. Appl. Math. (2018). [Google Scholar]
  • J. Nocedal and S.J. Wright, Numerical Optimization. Springer Science (2006). [Google Scholar]
  • Z.J. Shi and G. Sun, A diagonal-sparse quasi-Newton method for unconstrained optimization problem. J. Syst. Sci. Math. Sci. 26 (2006) 101–112. [Google Scholar]
  • Z. Wan, Y. Chen, S. Huang and D. Feng, A modified nonmonotone BFGS algorithm for solving smooth nonlinear equations. Optim. Lett. 8 (2014) 1845–1860. [Google Scholar]
  • M.Y. Waziri and Z. Abdul Majid, An improved diagonal Jacobian approximation via a new quasi-cauchy condition for solving large-scale systems of nonlinear equations. J. Appl. Math. 2013 (2013). [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. Stoch. 2 (2010) 54–63. [Google Scholar]
  • M.Y. Waziri, W.J. Leong, M. Mamat and A.U. Moyi, Two-step derivative-free diagonally Newton’s method for large-scale nonlinear equations. World Appl. Sci. J. 21 (2013) 86–94. [Google Scholar]
  • S. Wu and H. Wang, A modified Newton-like method for nonlinear equations. Comput. Appl. Math. 39 (2020) 1–18. [Google Scholar]
  • G. Yu, S. Niu and J. Ma, Multivariate spectral gradient projection method for nonlinear monotone equations with convex constraints. J. Ind. Manag. Optim. 9 (2013) 117–129. [Google Scholar]
  • G. Yuan and X. Lu, A new backtracking inexact BFGS method for symmetric nonlinear equations. Comput. Math. Appl. 55 (2008) 116–129. [Google Scholar]
  • L. Zhang, A derivative-free conjugate residual method using secant condition for general large-scale nonlinear equations. Numer. Algorithms 83 (2020) 1277–1293. [Google Scholar]

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