Accelerated Dai-Liao projection method for solving systems of monotone nonlinear equations with application to image deblurring

Ivanov, Branislav; Milovanović, Gradimir V.; Stanimirović, Predrag S.

doi:10.1007/s10898-022-01213-4

Cited by 14 publications

(5 citation statements)

References 62 publications

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“…where p ≥ 1 4 and q ≤ 0. Ivanov et al [24] used the search direction of the accelerated gradient descent method MSM [25] to generate the Dai-Liao conjugate condition parameter…”

Section: Motivation and Algorithmmentioning

confidence: 99%

A family of Dai-Liao conjugate gradient methods with strong convergence for Image restoration and Machine learning

Jiang,

Sun,

Jian

2024

Preprint

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Conjugate gradient method is one of the most effective schemes to deal with large-scale optimization problems. In this study, three classes of parameters for the Dai-Liao conjugate condition are provided to be chosen, and thus a new Dai-Liao conjugate parameter is derived. Making a truncation for the conjugate parameter and introducing a restart procedure into the search direction, a family of improved Dai-Liao conjugate gradient methods is proposed. It is sufficient descent at each iteration without depending on the choice of the line search criterion. Under usual assumptions, and using the weak Wolfe line search criterion to yield its steplength, its strong convergence is proved. Finally, choosing a specific algorithm from this family to solve large-scale unconstrained optimization problems, image restorations and machine learning, the corresponding numerical results show that the new algorithm is promising. Mathematics Subject Classification (2020) 65K05 · 90C52 · 90C53 · 90C56

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“…where p ≥ 1 4 and q ≤ 0. Ivanov et al [24] used the search direction of the accelerated gradient descent method MSM [25] to generate the Dai-Liao conjugate condition parameter…”

Section: Motivation and Algorithmmentioning

confidence: 99%

A family of Dai-Liao conjugate gradient methods with strong convergence for Image restoration and Machine learning

Jiang,

Sun,

Jian

2024

Preprint

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“…Based on a scalar approximation of the matrix 𝐹 ′ = ∇𝐹 yielding an adaptive formula for 𝑡, Halilu et al [58] proposed another CG algorithm of the DL family to solve the problem and evaluated its performance in robotics. Recently, in a similar scheme, an accelerated DL projection algorithm for solving the systems of monotone equations has been developed by Branislav et al [62].…”

Section: Nonlinear Systems Of Equationsmentioning

confidence: 99%

“…So, smooth relaxations of the image restoration model have been devised in the literature that can be addressed by large scale optimization algorithms [111]. As already mentioned, Babaie-Kafaki et al [6,31], Lu et al [79,80], Waziri et al [103] and Branislav et al [62] tackled the impulse noise removal of the images by the CG algorithms of the DL family.…”

Section: Image Restorationmentioning

confidence: 99%

A survey on the Dai–Liao family of nonlinear conjugate gradient methods

Babaie-Kafaki

2023

RAIRO-Oper. Res.

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At the beginning of this century, which is characterized by huge flows of emerging data, Dai and Liao proposed a pervasive conjugacy condition that triggered the interest of many optimization scholars. Recognized as a sophisticated conjugate gradient (CG) algorithm after about two decades, here we share our visions and thoughts on the method in the framework of a review study. In this regard, we first discuss the modified Dai–Liao methods based on the modified secant equations given in the literature, mostly with the aim of applying the objective function values in addition to the gradient information. Then, several adaptive, sort of optimal choices for the parameter of the method are studied. Especially, we devote a part of our study to the modified versions of the Hager–Zhang and Dai–Kou CG algorithms, being well-known members of the Dai–Liao class of CG methods. Extensions of the classical CG methods based on the Dai–Liao approach are also reviewed. Finally, we discuss the optimization models of practical disciplines that have been addressed by the Dai–Liao approach, including the nonlinear systems of equations, image restoration and compressed sensing.

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“…As an important area in digital image processing, 1 image restoration covers topics of image denoising, 2 – 4 deblurring, 5 – 7 medical imaging, 8 – 10 super-resolution reconstruction, 11 – 13 and so on. During the processes of acquisition and transmission, noise signals inevitably contaminate digital images.…”

Section: Introductionmentioning

confidence: 99%

Weighted structure tensor total variation for image denoising

Sheng,

Yang,

Chang

2024

J. Electron. Imag.

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Accelerated Dai-Liao projection method for solving systems of monotone nonlinear equations with application to image deblurring

Cited by 14 publications

References 62 publications

A family of Dai-Liao conjugate gradient methods with strong convergence for Image restoration and Machine learning

A family of Dai-Liao conjugate gradient methods with strong convergence for Image restoration and Machine learning

A survey on the Dai–Liao family of nonlinear conjugate gradient methods

Weighted structure tensor total variation for image denoising

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