Derivative-free SMR conjugate gradient method for constraint nonlinear equations

Volume 24, Issue 2, pp 147--164 http://dx.doi.org/10.22436/jmcs.024.02.06

Publication Date: January 23, 2021 Submission Date: August 03, 2020 Revision Date: December 13, 2020 Accteptance Date: January 02, 2021

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Authors

Abdulkarim Hassan Ibrahim - Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand. Kanikar Muangchoo - Department of Mathematics and Statistics, Faculty of Science and Technology, Rajamangala University of Technology Phra Nakhon (RMUTP), 1381 Pracharat 1 Road, Wongsawang, Bang Sue, Bangkok 10800, Thailand. Nur Syarafina Mohamed - Universiti Kuala Lumpur, Malaysian Institute of Industrial Technology, Malaysia. Auwal Bala Abubakar - Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University, Kano, Kano, Nigeria. - Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, Pretoria, Medunsa-0204, South Africa.

Abstract

Based on the SMR conjugate gradient method for unconstrained optimization proposed by Mohamed et al. [N. S. Mohamed, M. Mamat, M. Rivaie, S. M. Shaharuddin, Indones. J. Electr. Eng. Comput. Sci., \(\bf 11\) (2018), 1188--1193] and the Solodov and Svaiter projection technique, we propose a derivative-free SMR method for solving nonlinear equations with convex constraints. The proposed method can be viewed as an extension of the SMR method for solving unconstrained optimization. The proposed method can be used to solve large-scale nonlinear equations with convex constraints because of derivative-free and low storage. Under the assumption that the underlying mapping is Lipschitz continuous and satisfies a weaker monotonicity assumption, we prove its global convergence. Preliminary numerical results show that the proposed method is promising.

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Keywords

• Nonlinear equations
• conjugate gradient method
• projection method
• global convergence

MSC

•  65L09
•  65K05
•  90C30

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