A Solution Method for Nonlinear Monotone Equations via Hybrid Spectral Conjugate Gradient and Signal Recovery Problems

Aliyu Yusuf; Nibron Haggai Manjak; Hassan Mohammad; Aliyu Ibrahim Kiri; Auwal Bala Abubakar

doi:10.1007/s43069-024-00326-8

A Solution Method for Nonlinear Monotone Equations via Hybrid Spectral Conjugate Gradient and Signal Recovery Problems

Aliyu Yusuf^*, Nibron Haggai Manjak, Hassan Mohammad, Aliyu Ibrahim Kiri, Auwal Bala Abubakar

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we propose a method via hybrid spectral conjugate gradient to solve nonlinear monotone equations and signal recovery problems. This has been done using the hybrid conjugate gradient (CG) parameters of Dai-Yuan (DY), conjugate descent (CD), Hestenes-Stiefel (HS), Liu-Storey (LS) and the corresponding search direction of spectral conjugate gradient method. The search direction has proved to be adequately descent regardless of the step-size. Under reasonable assumptions, the convergence of the algorithm is established. Additionally, numerical tests are run on a set of benchmark test problems to illustrate the effectiveness and competitiveness of the new algorithm compared with other existing alternatives. Finally, some applications of the proposed algorithm are explored.

Original language	English
Article number	49
Journal	Operations Research Forum
Volume	5
Issue number	2
DOIs	https://doi.org/10.1007/s43069-024-00326-8
Publication status	Published - Jun 2024
Externally published	Yes

Keywords

Conjugate gradient method
Global convergence
Nonlinear monotone equations
Numerical experiments
Spectral gradient parameter

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10.1007/s43069-024-00326-8

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title = "A Solution Method for Nonlinear Monotone Equations via Hybrid Spectral Conjugate Gradient and Signal Recovery Problems",

abstract = "In this paper, we propose a method via hybrid spectral conjugate gradient to solve nonlinear monotone equations and signal recovery problems. This has been done using the hybrid conjugate gradient (CG) parameters of Dai-Yuan (DY), conjugate descent (CD), Hestenes-Stiefel (HS), Liu-Storey (LS) and the corresponding search direction of spectral conjugate gradient method. The search direction has proved to be adequately descent regardless of the step-size. Under reasonable assumptions, the convergence of the algorithm is established. Additionally, numerical tests are run on a set of benchmark test problems to illustrate the effectiveness and competitiveness of the new algorithm compared with other existing alternatives. Finally, some applications of the proposed algorithm are explored.",

keywords = "Conjugate gradient method, Global convergence, Nonlinear monotone equations, Numerical experiments, Spectral gradient parameter",

author = "Aliyu Yusuf and Manjak, {Nibron Haggai} and Hassan Mohammad and Kiri, {Aliyu Ibrahim} and Abubakar, {Auwal Bala}",

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T1 - A Solution Method for Nonlinear Monotone Equations via Hybrid Spectral Conjugate Gradient and Signal Recovery Problems

AU - Yusuf, Aliyu

AU - Manjak, Nibron Haggai

AU - Mohammad, Hassan

AU - Kiri, Aliyu Ibrahim

AU - Abubakar, Auwal Bala

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.

PY - 2024/6

Y1 - 2024/6

N2 - In this paper, we propose a method via hybrid spectral conjugate gradient to solve nonlinear monotone equations and signal recovery problems. This has been done using the hybrid conjugate gradient (CG) parameters of Dai-Yuan (DY), conjugate descent (CD), Hestenes-Stiefel (HS), Liu-Storey (LS) and the corresponding search direction of spectral conjugate gradient method. The search direction has proved to be adequately descent regardless of the step-size. Under reasonable assumptions, the convergence of the algorithm is established. Additionally, numerical tests are run on a set of benchmark test problems to illustrate the effectiveness and competitiveness of the new algorithm compared with other existing alternatives. Finally, some applications of the proposed algorithm are explored.

AB - In this paper, we propose a method via hybrid spectral conjugate gradient to solve nonlinear monotone equations and signal recovery problems. This has been done using the hybrid conjugate gradient (CG) parameters of Dai-Yuan (DY), conjugate descent (CD), Hestenes-Stiefel (HS), Liu-Storey (LS) and the corresponding search direction of spectral conjugate gradient method. The search direction has proved to be adequately descent regardless of the step-size. Under reasonable assumptions, the convergence of the algorithm is established. Additionally, numerical tests are run on a set of benchmark test problems to illustrate the effectiveness and competitiveness of the new algorithm compared with other existing alternatives. Finally, some applications of the proposed algorithm are explored.

KW - Conjugate gradient method

KW - Global convergence

KW - Nonlinear monotone equations

KW - Numerical experiments

KW - Spectral gradient parameter

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DO - 10.1007/s43069-024-00326-8

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JO - Operations Research Forum

JF - Operations Research Forum

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ER -

A Solution Method for Nonlinear Monotone Equations via Hybrid Spectral Conjugate Gradient and Signal Recovery Problems

Abstract

Keywords

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