Communications in Mathematical Sciences

Volume 21 (2023)

Number 2

A derivative-free conjugate gradient method for large-scale nonlinear systems of monotone equations

Pages: 543 – 557

DOI: https://dx.doi.org/10.4310/CMS.2023.v21.n2.a11

Authors

Jing Gao (School of Mathematics and Statistics, Beihua University, Jilin, China)

Yanran Li (School of Mathematics and Statistics, Beihua University, Jilin, China)

Mingyuan Cao (School of Mathematics and Statistics, Beihua University, Jilin, China)

Yueting Yang (School of Mathematics and Statistics, Beihua University, Jilin, China; and School of Science, Jiangsu University, Zhenjiang, Jiangsu, China)

Xue Bai (School of Mathematics and Statistics, Beihua University, Jilin, China)

Abstract

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.

Keywords

derivative-free technique, nonlinear systems of monotone equations, projection technology, conjugate gradient method

2010 Mathematics Subject Classification

65K05, 65K10, 90C06, 90C56

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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