An Inexact PRP Conjugate Gradient Method for Symmetric Nonlinear Equations

In this article, without computing exact gradient and Jacobian, we proposed a derivative-free Polak-Ribière-Polyak (PRP) method for solving nonlinear equations whose Jacobian is symmetric. This method is a generalization of the classical PRP method for unconstrained optimization problems. By utilizi...

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Bibliographic Details
Published in:Numerical functional analysis and optimization 2014-03, Vol.35 (3), p.370-388
Main Authors: Zhou, Weijun, Shen, Dongmei
Format: Article
Language:English
Subjects:
Backtracking line search
Conjugate gradient method
Convergence
Global convergence
Jacobians
Mathematical analysis
Mathematical models
Nonlinear equations
Optimization
PRP method
Smoothing
Symmetric nonlinear equations
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Summary:In this article, without computing exact gradient and Jacobian, we proposed a derivative-free Polak-Ribière-Polyak (PRP) method for solving nonlinear equations whose Jacobian is symmetric. This method is a generalization of the classical PRP method for unconstrained optimization problems. By utilizing the symmetric structure of the system sufficiently, we prove global convergence of the proposed method with some backtracking type line search under suitable assumptions. Moreover, we extend the proposed method to nonsmooth equations by adopting the smoothing technique. We also report some numerical results to show its efficiency.
ISSN:0163-0563
1532-2467
DOI:10.1080/01630563.2013.871290