• Corpus ID: 245837009

A multivariate spectral hybridization of HS and PRP method for nonlinear systems of equations

@inproceedings{Mohammad2022AMS,
  title={A multivariate spectral hybridization of HS and PRP method for nonlinear systems of equations},
  author={Hassan Mohammad},
  year={2022}
}
We present a multivariate spectral hybridization of Hestenes-Stiefel (HS) and Polak–Ribière– Polyak (PRP) method for solving large-scale nonlinear systems of equations. The search direction of the method is obtained by incorporating a multivariate spectral approach with the positive hybridization of Hestenes-Stiefel and Polak–Ribière–Polyak parameters (HS & PRP hybrid+). By employing a derivative-free nonmonotone line search technique, the global convergence of the sequence generated by the… 

References

SHOWING 1-10 OF 44 REFERENCES
A new nonmonotone spectral residual method for nonsmooth nonlinear equations
A derivative-free PRP method for solving large-scale nonlinear systems of equations and its global convergence
  • Min Li
  • Mathematics
    Optim. Methods Softw.
  • 2014
An extended Polak-Ribière-Polyak conjugate gradient method for solving nonlinear systems of equations is proposed, which is suitable to large-scale problems for the lower storage requirement. Under
A modified Hestenes–Stiefel conjugate gradient method with an optimal property
In this paper, based on the numerical efficiency of Hestenes–Stiefel (HS) method, a new modified HS algorithm is proposed for unconstrained optimization. The new direction independent of the line
A derivative-free method for solving large-scale nonlinearsystems of equations
In this paper, a fully derivative-free method for solving large-scale nonlinear systems of equations is presented. It uses in a systematic way the well-known Polak-Ribiere-Polyak (PRP) conjugate
A descent hybrid modification of the Polak-Ribière-Polyak conjugate gradient method
TLDR
Comparing the proposed nonlinear conjugate gradient method with the hybridizing self-adjusting approach of Dong et al. and three-term formulation shows computational efficiency in the sense of Dolan–More performance profile.
A Projection Hestenes–Stiefel Method with Spectral Parameter for Nonlinear Monotone Equations and Signal Processing
TLDR
The proposed modified conjugate gradient method is applied to solve some benchmark monotone nonlinear equations and also extended to solve l 1 -norm regularized problems to reconstruct a sparse signal in compressive sensing.
An Inexact PRP Conjugate Gradient Method for Symmetric Nonlinear Equations
TLDR
A derivative-free Polak-Ribière-Polyak (PRP) method for solving nonlinear equations whose Jacobian is symmetric is proposed, which is a generalization of the classical PRP method for unconstrained optimization problems.
...
...