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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*
Affiliation:
College of Sciences, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China Department of Mathematics, Huzhou University, Huzhou 313000, China email [email protected]
QIN NI
Affiliation:
College of Sciences, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China email [email protected]
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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.

Type
Research Article
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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