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January  2010, 6(1): 149-160. doi: 10.3934/jimo.2010.6.149

A derivative-free method for solving large-scale nonlinear systems of equations

Gaohang Yu 1,

1. 

Jiangxi Key Laboratory of Numerical Simulation Technology, School of Mathematics and Computer Sciences, Gannan Normal University, Ganzhou, 341000, China

Received  July 2009 Revised  September 2009 Published  November 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-Ribière-Polyak (PRP) conjugate gradient direction as a search direction and employs a backtracking process to obtain a suitable stepsize. Assume that the nonlinear mapping is Lipschitz continuous, some global convergence results are established. A modification of this method which may allow the objective function's sufficiently nonmonotone behavior is also presented in this paper. Numerical comparisons using a set of large-scale test problems in the CUTE library show that the proposed methods are encouraging.
Keywords: conjugate gradient method, nonlinear systems, derivative-free method..
Mathematics Subject Classification: Primary: 65H10, 65K05 Secondary: 90C2.
Citation: Gaohang Yu. A derivative-free method for solving large-scale nonlinear systems of equations. Journal of Industrial & Management Optimization, 2010, 6 (1) : 149-160. doi: 10.3934/jimo.2010.6.149
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