Projection Method for Solving Large-scale System of Nonlinear Equations

Authors

  • Wiyada Kumam Applied Mathematics for Science and Engineering Research Unit (AMSERU), Program in Applied Statistics, Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Pathum Thani 12110, Thailand https://orcid.org/0000-0001-8773-4821
  • Jesus Vigo-Aguiar Department of Applied Mathematics, University of Salamanca, Salamanca, Spain https://orcid.org/0000-0002-1921-6579
  • Poom Kumam Department of Mathematics King Mongkut’s University of Technology Thonburi (KMUTT) 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand https://orcid.org/0000-0002-5463-4581

DOI:

https://doi.org/10.58715/ncao.2023.2.5

Keywords:

Nonlinear equations, Projection method, Derivative-free method, Global convergence

Abstract

Derivative-free projection methods have proven to be highly effective and valuable in solving large-scale systems of nonlinear equations (SNE). Extensive research is continuously being conducted to enhance existing methods and develop new projection methods. In this paper, we modified the conjugate gradient parameter proposed by Zhu et al. and extend it to solve SNE with convex constrain. The advantage of the proposed method is that it does not rely on Jacobian information and does not require the storage of any matrices at each iteration. This characteristic makes it well-suited for tackling large-scale non-smooth problems. Under appropriate conditions, we show that the proposed method is globally convergent. Numerical experiments were conducted to evaluate the effectiveness of the proposed method and compare it with other approaches.

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Published

2023-12-30

How to Cite

Kumam, W., Vigo-Aguiar, J., & Kumam, P. (2023). Projection Method for Solving Large-scale System of Nonlinear Equations. Nonlinear Convex Analysis and Optimization: An International Journal on Numerical, Computation and Applications, 2(2), 93–112. https://doi.org/10.58715/ncao.2023.2.5

Issue

Vol. 2 No. 2 (2023): July - December, 2023

Section

Articles

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Copyright (c) 2023 Wiyada Kumam, Jesus Vigo-Aguiar, Poom Kumam

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