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A NEW DERIVATIVE-FREE CONJUGATE GRADIENT METHOD FOR LARGE-SCALE NONLINEAR SYSTEMS OF EQUATIONS

Published online by Cambridge University Press:  22 March 2017

XIAOWEI FANG  and
QIN NI
XIAOWEI FANG*
Affiliation:
College of Sciences, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China Department of Mathematics, Huzhou University, Huzhou 313000, China email fangxiaowei@163.com
QIN NI
Affiliation:
College of Sciences, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China email niqfs@nuaa.edu.cn
*
✉fangxiaowei@163.com
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Abstract

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We propose a new derivative-free conjugate gradient method for large-scale nonlinear systems of equations. The method combines the Rivaie–Mustafa–Ismail–Leong conjugate gradient method for unconstrained optimisation problems and a new nonmonotone line-search method. The global convergence of the proposed method is established under some mild assumptions. Numerical results using 104 test problems from the CUTEst test problem library show that the proposed method is promising.

Keywords

large-scale nonlinear systems of equationsconjugate gradient methodnonmonotone line search

MSC classification

Primary: 90C56: Derivative-free methods and methods using generalized derivatives
Secondary: 90C30: Nonlinear programming
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 95 , Issue 3 , June 2017 , pp. 500 - 511
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

Footnotes

This work was supported by the National Natural Science Foundation of China (11071117, 11274109), the Natural Science Foundation of Jiangsu Province (BK20141409), and the Natural Science Foundation of Huzhou University (KX21072).

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