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Communications in Mathematical Sciences
Volume 21 (2023)
A derivative-free conjugate gradient method for large-scale nonlinear systems of monotone equations
Pages: 543 – 557
This paper presents a derivative-free conjugate gradient type algorithm for large-scale nonlinear systems of monotone equations. New search directions with superior numerical performance are constructed by introducing a new conjugate parameter and particular spectral parameters. These search directions inherit the numerical stability of RMIL search direction and satisfy the sufficient descent condition independent of step size. The method combines the hyperplane projection and the derivative-free line search technique to compute the iteration points. Under some appropriate assumptions, the global convergence of the given methods is established. Numerical experiments indicate that the proposed algorithms are effective.
derivative-free technique, nonlinear systems of monotone equations, projection technology, conjugate gradient method
2010 Mathematics Subject Classification
65K05, 65K10, 90C06, 90C56
This work is supported by the key project of natural science foundation joint fund of Jilin Province (YDZJ202101ZYTS167, YDZJ202201ZYTS303); by the innovation talent training program of science and technology of Jilin Province (20180519011JH); by the science and technology development project program of Jilin Province (20190303132SF); by the youth growth science and technology project of the Jilin Province science and technology development plan; by the PhD start-up fund of natural science foundation of Beihua University; and by the project of education department of Jilin Province (JJKH202100 30KJ, JJKH20230054KJ).
Received 5 September 2021
Accepted 20 June 2022
Published 1 February 2023