A scaled Polak-Ribi$ \grave{e} $re-Polyak conjugate gradient algorithm for constrained nonlinear systems and motion control

Jamilu Sabi'u; Ali Althobaiti; Saad Althobaiti; Soubhagya Kumar Sahoo; Thongchai Botmart; Jamilu Sabi'u; Ali Althobaiti; Saad Althobaiti; Soubhagya Kumar Sahoo; Thongchai Botmart

doi:10.3934/math.2023241

AIMS Mathematics

2023, Volume 8, Issue 2: 4843-4861. doi: 10.3934/math.2023241

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Research article

A scaled Polak-Ribi$ \grave{e} $re-Polyak conjugate gradient algorithm for constrained nonlinear systems and motion control

1.
Department of Mathematics, Yusuf Maitama Sule University Kano, PMB 3220, Kano Nigeria
2.
Mathematics Department, College of Science, Taif University, P.O.Box 11099, Taif 21944, Saudi Arabia
3.
Department of Sciences and Technology, Ranyah University Collage, Taif University, P.O.Box 11099, Taif 21944, Saudi Arabia
4.
Department of Mathematics, Institute of Technical Education and Research, Siksha O Anusandhan University, Bhubaneswar 751030, Odisha, India
5.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Received: 14 September 2022 Revised: 15 November 2022 Accepted: 05 December 2022 Published: 09 December 2022
MSC : 90C26, 90C30

This paper proposes Polak-Ribi$ \grave{e} $re-Polyak (PRP) conjugate gradient (CG) directions based on two efficient scaling strategies. The first scaling parameter is determined by approaching the quasi-Newton direction, and the second by utilizing the well-known Barzilai-Borwein approach. In addition, we proposed two directions that satisfy the sufficient descent criterion regardless of the line search strategy. The proposed directions lead to a matrix-free algorithm for solving monotone-constrained nonlinear systems. The proposed algorithm's global convergence analysis is presented using some underlying assumptions. Furthermore, a detailed numerical comparison with other existing algorithms revealed that the proposed algorithm is both efficient and effective. Finally, the proposed technique is applied to the motion control problem of a two-joint planar robotic manipulator.
- convex constrained monotone systems,
- scaled conjugate gradient method,
- sufficient descent condition,
- Barzilai-Borwein approach
Citation: Jamilu Sabi'u, Ali Althobaiti, Saad Althobaiti, Soubhagya Kumar Sahoo, Thongchai Botmart. A scaled Polak-Ribi$ \grave{e} $re-Polyak conjugate gradient algorithm for constrained nonlinear systems and motion control[J]. AIMS Mathematics, 2023, 8(2): 4843-4861. doi: 10.3934/math.2023241

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Abstract

This paper proposes Polak-Ribi$ \grave{e} $re-Polyak (PRP) conjugate gradient (CG) directions based on two efficient scaling strategies. The first scaling parameter is determined by approaching the quasi-Newton direction, and the second by utilizing the well-known Barzilai-Borwein approach. In addition, we proposed two directions that satisfy the sufficient descent criterion regardless of the line search strategy. The proposed directions lead to a matrix-free algorithm for solving monotone-constrained nonlinear systems. The proposed algorithm's global convergence analysis is presented using some underlying assumptions. Furthermore, a detailed numerical comparison with other existing algorithms revealed that the proposed algorithm is both efficient and effective. Finally, the proposed technique is applied to the motion control problem of a two-joint planar robotic manipulator.

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