Applications of two sufficient descent spectral conjugate gradient methods in image denoising

Yu Cai; Hong Yue; Chenyun Mo; Yu Cai; Hong Yue; Chenyun Mo

doi:10.3934/math.2026355

AIMS Mathematics

2026, Volume 11, Issue 3: 8635-8654. doi: 10.3934/math.2026355

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Applications of two sufficient descent spectral conjugate gradient methods in image denoising

Yu Cai ¹,
Hong Yue ²,
Chenyun Mo ^{1
,
,}

1.
School of Education, Huaibei Institute of Technology, Huaibei 235000, Anhui, China
2.
Department of Basic Courses, Liaoning Finance and Trade College, Xingcheng 125105, Liaoning, China

Received: 06 January 2026 Revised: 19 March 2026 Accepted: 23 March 2026 Published: 31 March 2026
MSC : 65K10, 68U10, 90C30

To solve large-scale unconstrained optimization problems, this paper further investigated the RMIL conjugate gradient method and its variants in order to propose two new spectral conjugate gradient methods. Under basic assumptions for unconstrained optimization problems, where the level set was bounded and the gradient was Lipschitz continuous, the search directions generated by the proposed methods satisfied the sufficient descent property independent of the choice of line search. Moreover, the global convergence of the methods was established under both the standard Wolfe line search and the standard Armijo line search. Numerical experiments on unconstrained optimization and image denoising problems under both line searches demonstrated that the two proposed spectral conjugate gradient methods exhibited superior performance and broader applicability.
- unconstrained optimization,
- spectral conjugate gradient methods,
- sufficient descent property,
- global convergence,
- image denoising
Citation: Yu Cai, Hong Yue, Chenyun Mo. Applications of two sufficient descent spectral conjugate gradient methods in image denoising[J]. AIMS Mathematics, 2026, 11(3): 8635-8654. doi: 10.3934/math.2026355

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Abstract

To solve large-scale unconstrained optimization problems, this paper further investigated the RMIL conjugate gradient method and its variants in order to propose two new spectral conjugate gradient methods. Under basic assumptions for unconstrained optimization problems, where the level set was bounded and the gradient was Lipschitz continuous, the search directions generated by the proposed methods satisfied the sufficient descent property independent of the choice of line search. Moreover, the global convergence of the methods was established under both the standard Wolfe line search and the standard Armijo line search. Numerical experiments on unconstrained optimization and image denoising problems under both line searches demonstrated that the two proposed spectral conjugate gradient methods exhibited superior performance and broader applicability.

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