Open Access
Issue
RAIRO-Oper. Res.
Volume 59, Number 1, January-February 2025
Page(s) 609 - 624
DOI https://doi.org/10.1051/ro/2024234
Published online 14 February 2025
  • J.G.P. Barnes, An algorithm for solving nonlinear equations based on the secant method. Comput. J. 8 (1965) 66–72. [CrossRef] [MathSciNet] [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]
  • E.G. Birgin and J.M. Martínez, Secant acceleration of sequential residual methods for solving large-scale nonlinear systems of equations. SIAM J. Numer. Anal. 60 (2022) 3145–3180. [CrossRef] [MathSciNet] [Google Scholar]
  • E.G. Birgin, J.M. Martínez and M. Raydan, Nonmonotone spectral projected gradient methods on convex sets. SIAM J. Optim. 10 (2000) 1196–1211. [CrossRef] [MathSciNet] [Google Scholar]
  • E.G. Birgin, J.M. Martínez and M. Raydan, Algorithm 813: SPG – software for convex-constrained optimization. ACM Trans. Math. Softw. 27 (2001) 340–349. [CrossRef] [Google Scholar]
  • E.G. Birgin, J.M. Martínez and M. Raydan, Spectral projected gradient methods, in Encyclopedia of Optimization, edited by C.A. Floudas and P.M. Pardalos. Springer US, Boston, MA (2009) 3652–3659. [Google Scholar]
  • E.G. Birgin, J.M. Martínez and M. Raydan, Spectral projected gradient methods: review and perspectives. J. Stat. Softw. 60 (2014) 1–21. [CrossRef] [Google Scholar]
  • R.H. Byrd, P. Lu and J. Nocedal, A limited memory algorithm for bound constrained optimization. SIAM J. Sci. Stat. Comput. 16 (1995) 1190–1208. [CrossRef] [Google Scholar]
  • A.R. Conn, N.I.M. Gould and P.L. Toint, Lancelot – A Fortran Package for Large-Scale Nonlinear Optimization (Release A). Springer, Berlin, Heidelberg (1992). [Google Scholar]
  • J.E. Dennis and R.B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Society for Industrial and Applied Mathematics, Philadelphia, PA (1996). [Google Scholar]
  • E.D. Dolan and J.J. Moré, Benchmarking optimization software with performance profiles. Math. Prog. 91 (2002) 201–213. [CrossRef] [Google Scholar]
  • N.I.M. Gould, D. Orban and P.L. Toint, CUTEst: a Constrained and Unconstrained Testing Environment with safe threads for mathematical optimization. Comput. Optim. App. 60 (2015) 545–557. [CrossRef] [Google Scholar]
  • W. Hock and K. Schittkowski, Test Examples for Nonlinear Programming Codes. Vol. 187 of Lecture Notes in Economics and Mathematical Systems. Springer, Berlin, Heidelberg (1981). [CrossRef] [Google Scholar]
  • C.T. Kelley, Iterative Methods for Linear and Nonlinear Equations. Society for Industrial and Applied Mathematics, Philadelphia, PA (1995). [CrossRef] [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. Martínez and M. Raydan, Spectral residual method without gradient information for solving large-scale nonlinear systems of equations. Math. Comput. 75 (2006) 1429–1448. [CrossRef] [Google Scholar]
  • J.J. Moré, B.S. Garbow and K.E. Hillstrom, Testing unconstrained optimization software. ACM Trans. Math. Softw. 7 (1981) 17–41. [CrossRef] [Google Scholar]
  • M. Pernice and H.F. Walker, Nitsol: a newton iterative solver for nonlinear systems. SIAM J. Sci. Comput. 19 (1998) 302–318. [CrossRef] [MathSciNet] [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] [MathSciNet] [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]
  • W.C. Rheinboldt, Methods for Solving Systems of Nonlinear Equations. Society for Industrial and Applied Mathematics, Philadelphia, PA (1998). [CrossRef] [Google Scholar]
  • K. Schittkowski, More Test Examples for Nonlinear Programming Codes. Vol. 282 of Lecture Notes in Economics and Mathematical Systems. Springer, Berlin, Heidelberg (1987). [CrossRef] [Google Scholar]
  • The R Core Team, R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria (2009). [Google Scholar]
  • R. Varadhan and P. Gilbert, BB: an R package for solving a large system of nonlinear equations and for optimizing a high-dimensional nonlinear objective function. J. Stat. Softw. 32 (2009) 1–26. [CrossRef] [Google Scholar]
  • P. Wolfe, The secant method for simultaneous nonlinear equations. Commun. ACM 2 (1959) 12–13. [CrossRef] [Google Scholar]

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