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…
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SHOWING 1-10 OF 44 REFERENCES
A Polak-Ribière-Polyak method for solving large-scale nonlinear systems of equations and its global convergence
- MathematicsAppl. Math. Comput.
- 2014
A new nonmonotone spectral residual method for nonsmooth nonlinear equations
- Mathematics, Computer ScienceJ. Comput. Appl. Math.
- 2017
A derivative-free PRP method for solving large-scale nonlinear systems of equations and its global convergence
- MathematicsOptim. 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
- Computer ScienceOptim. Methods Softw.
- 2019
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
- Mathematics
- 2009
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
- Computer ScienceRAIRO Oper. Res.
- 2016
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 nonmonotone PRP conjugate gradient method for solving square and under-determined systems of equations
- MathematicsComput. Math. Appl.
- 2017
A family of derivative-free conjugate gradient methods for large-scale nonlinear systems of equations
- Mathematics
- 2009
A Projection Hestenes–Stiefel Method with Spectral Parameter for Nonlinear Monotone Equations and Signal Processing
- Mathematics
- 2020
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
- Mathematics, Computer Science
- 2014
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.