An efficient spectral minimization of the Dai-Yuan method with application to image reconstruction

Nasiru Salihu; Poom Kumam; Ibrahim Mohammed Sulaiman; Thidaporn Seangwattana; Nasiru Salihu; Poom Kumam; Ibrahim Mohammed Sulaiman; Thidaporn Seangwattana

doi:10.3934/math.20231583

AIMS Mathematics

2023, Volume 8, Issue 12: 30940-30962. doi: 10.3934/math.20231583

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Research article

An efficient spectral minimization of the Dai-Yuan method with application to image reconstruction

1.
Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Fixed Point Research Laboratory, Fixed Point Theory and Applications Research Group, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangkok 10140, Thailand
2.
Department of Mathematics, Faculty of Sciences, Modibbo Adama University, Yola 652105, Nigeria
3.
KMUTT-Fixed Point Research Laboratory, Room SCL 802, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangkok 10140, Thailand
4.
Institute of Strategic Industrial Decision Modelling, School of Quantitative Sciences, Universiti Utara Malaysia, Sintok, Kedah 06010, Malaysia
5.
Faculty of Education and Arts, Sohar University, Sohar 311, Oman
6.
Faculty of Science Energy and Environment, King Mongkut's University of Technology North Bangkok, Rayong Campus (KMUTNB), Rayong 21120, Thailand

Received: 16 August 2023 Revised: 24 September 2023 Accepted: 13 October 2023 Published: 17 November 2023
MSC : 65K05, 90C06, 90C30, 90C47, 90C90

In this paper, a spectral Dai and Yuan conjugate gradient (CG) method is proposed based on the generalized conjugacy condition for large-scale unconstrained optimization, in which the spectral parameter is motivated by some interesting theoretical features of quadratic convergence associated with the Newton method. Accordingly, utilizing the strong Wolfe line search to yield the step-length, the search direction of the proposed spectral method is sufficiently descending and converges globally. By applying some standard Euclidean optimization test functions, numerical results reports show the advantage of the method over some modified Dai and Yuan CG schemes in literature. In addition, the method also shows some reliable results, when applied to solve an image reconstruction model.
- unconstrained optimization,
- spectral conjugate gradient method,
- generalized conjugacy condition,
- Newton direction,
- global convergence,
- image reconstruction
Citation: Nasiru Salihu, Poom Kumam, Ibrahim Mohammed Sulaiman, Thidaporn Seangwattana. An efficient spectral minimization of the Dai-Yuan method with application to image reconstruction[J]. AIMS Mathematics, 2023, 8(12): 30940-30962. doi: 10.3934/math.20231583

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Abstract

In this paper, a spectral Dai and Yuan conjugate gradient (CG) method is proposed based on the generalized conjugacy condition for large-scale unconstrained optimization, in which the spectral parameter is motivated by some interesting theoretical features of quadratic convergence associated with the Newton method. Accordingly, utilizing the strong Wolfe line search to yield the step-length, the search direction of the proposed spectral method is sufficiently descending and converges globally. By applying some standard Euclidean optimization test functions, numerical results reports show the advantage of the method over some modified Dai and Yuan CG schemes in literature. In addition, the method also shows some reliable results, when applied to solve an image reconstruction model.

References

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