A new spectral method with inertial technique for solving system of nonlinear monotone equations and applications

Sani Aji; Aliyu Muhammed Awwal; Ahmadu Bappah Muhammadu; Chainarong Khunpanuk; Nuttapol Pakkaranang; Bancha Panyanak; Sani Aji; Aliyu Muhammed Awwal; Ahmadu Bappah Muhammadu; Chainarong Khunpanuk; Nuttapol Pakkaranang; Bancha Panyanak

doi:10.3934/math.2023221

AIMS Mathematics

2023, Volume 8, Issue 2: 4442-4466. doi: 10.3934/math.2023221

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Research article

A new spectral method with inertial technique for solving system of nonlinear monotone equations and applications

1.
Department of Mathematics, Faculty of Science, Gombe State University (GSU), Gombe, Nigeria
2.
GSU-Mathematics for Innovative Research Group, Gombe State University (GSU), Gombe, Nigeria
3.
Mathematics and Computing Science Program, Faculty of Science and Technology, Phetchabun Rajabhat University, Phetchabun 67000, Thailand
4.
Research Group in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
5.
Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Received: 27 July 2022 Revised: 13 November 2022 Accepted: 23 November 2022 Published: 05 December 2022
MSC : 90C30, 90C06, 90C56

Many problems arising from science and engineering are in the form of a system of nonlinear equations. In this work, a new derivative-free inertial-based spectral algorithm for solving the system is proposed. The search direction of the proposed algorithm is defined based on the convex combination of the modified long and short Barzilai and Borwein spectral parameters. Also, an inertial step is introduced into the search direction to enhance its efficiency. The global convergence of the proposed algorithm is described based on the assumption that the mapping under consideration is Lipschitz continuous and monotone. Numerical experiments are performed on some test problems to depict the efficiency of the proposed algorithm in comparison with some existing ones. Subsequently, the proposed algorithm is used on problems arising from robotic motion control.
- derivative-free method,
- spectral gradient method,
- inertial step,
- nonlinear monotone equations
Citation: Sani Aji, Aliyu Muhammed Awwal, Ahmadu Bappah Muhammadu, Chainarong Khunpanuk, Nuttapol Pakkaranang, Bancha Panyanak. A new spectral method with inertial technique for solving system of nonlinear monotone equations and applications[J]. AIMS Mathematics, 2023, 8(2): 4442-4466. doi: 10.3934/math.2023221

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Abstract

Many problems arising from science and engineering are in the form of a system of nonlinear equations. In this work, a new derivative-free inertial-based spectral algorithm for solving the system is proposed. The search direction of the proposed algorithm is defined based on the convex combination of the modified long and short Barzilai and Borwein spectral parameters. Also, an inertial step is introduced into the search direction to enhance its efficiency. The global convergence of the proposed algorithm is described based on the assumption that the mapping under consideration is Lipschitz continuous and monotone. Numerical experiments are performed on some test problems to depict the efficiency of the proposed algorithm in comparison with some existing ones. Subsequently, the proposed algorithm is used on problems arising from robotic motion control.

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