dfsaneacc-package {dfsaneacc}

Accelerated Derivative-Free Method for Large-Scale Nonlinear Systems of Equations

Description

Secant acceleration applied to derivative-free Spectral Residual Methods for solving large-scale nonlinear systems of equations. The main reference follows: E. G. Birgin and J. M. Martinez (2022) <doi:10.1137/20M1388024>.

Details

This package includes the function:

    dfsaneacc function to solve large-scale nonlinear systems of
              equations using a derivative-free approach with sequential
              secant acceleration for spectral residual methods.
  

Author(s)

Ernesto G. Birgin [aut, ctb], John L. Gardenghi [aut, cre, ctb, trl], Diaulas S. Marcondes [aut, ctb, trl], Jose M. Martinez [aut, ctb]

Maintainer: John L. Gardenghi <[e-mail]>

References

J. Barzilai, and J. M. Borwein (1988), Two-point step size gradient methods, IMA J Numerical Analysis, 8, 141-148.

E. G. Birgin, J. M. Mart\'inez (2022), Secant acceleration of sequential residual methods for solving large-scale nonlinear systems of equations, SIAM Journal on Numerical Analysis, 60(6), 3145-3180.

W. LaCruz, and M. Raydan (2003), Nonmonotone spectral methods for large-scale nonlinear systems, Optimization Methods and Software, 18, 583-599.

W. LaCruz, J. M. Mart\'inez, and M. Raydan (2006), Spectral residual method without gradient information for solving large-scale nonlinear systems of equations, Mathematics of Computation, 75, 1429-1448.

M. Raydan (1997), Barzilai-Borwein gradient method for large-scale unconstrained minimization problem, SIAM Journal on Optimization, 7, 26-33.