A Family of Derivative-Free Conjugate Gradient Methods for Constrained Nonlinear Equations and Image Restoration

Ibrahim, Abdulkarim Hassan; Kumam, Wiyada

doi:10.1109/access.2020.3020969

Cited by 45 publications

(12 citation statements)

References 50 publications

(64 reference statements)

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“…Considering the simplicity and low storage requirement of the conjugate gradient method [20,21], several researchers combined the projection technique of Solodov and Svaiter [56] with the conjugate gradient methods to solve large-scale nonlinear equations, see [38,13,42,40,43,1,7,45,41,12,47,10,9,46,39,52,2,3,8,53,11,37,44,4,6,36] and references therein. Based on the projection method, Gao and He [35] introduced an efficient three-term derivative-free method for solving nonlinear monotone equations with convex constraints (1) by choosing a part of the Liu-Storey (LS) conjugate parameter as a new conjugate parameter.…”

Section: Introductionmentioning

confidence: 99%

Projection method with inertial step for nonlinear equations: Application to signal recovery

Ibrahim

Sun

Chaipunya

et al. 2023

JIMO

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<p style='text-indent:20px;'>In this paper, using the concept of inertial extrapolation, we introduce a globally convergent inertial extrapolation method for solving nonlinear equations with convex constraints for which the underlying mapping is monotone and Lipschitz continuous. The method can be viewed as a combination of the efficient three-term derivative-free method of Gao and He [Calcolo. 55(4), 1-17, 2018] with the inertial extrapolation step. Moreover, the algorithm is designed such that at every iteration, the method is free from derivative evaluations. Under standard assumptions, we establish the global convergence results for the proposed method. Numerical implementations illustrate the performance and advantage of this new method. Moreover, we also extend this method to solve the LASSO problems to decode a sparse signal in compressive sensing. Performance comparisons illustrate the effectiveness and competitiveness of our algorithm.</p>

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Section: Introductionmentioning

confidence: 99%

Projection method with inertial step for nonlinear equations: Application to signal recovery

Ibrahim

Sun

Chaipunya

et al. 2023

JIMO

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“…where Υ is the linear operator, • 1 represents the l 1 norm, and λ is the regularization parameter used to weigh the data item and the regularization term. Many works have focused on the image restoration problem, and more detailed references can be found in [31][32][33][34]. In this paper, we display the original image to be repaired, and the repaired results of DSCG, TTS, and CG_DESCENT from left to right.…”

Section: Image Restoration Problemmentioning

confidence: 99%

A Dynamically Adjusted Subspace Gradient Method and Its Application in Image Restoration

Huo

Xia

et al. 2021

Symmetry

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In this paper, a new subspace gradient method is proposed in which the search direction is determined by solving an approximate quadratic model in which a simple symmetric matrix is used to estimate the Hessian matrix in a three-dimensional subspace. The obtained algorithm has the ability to automatically adjust the search direction according to the feedback from experiments. Under some mild assumptions, we use the generalized line search with non-monotonicity to obtain remarkable results, which not only establishes the global convergence of the algorithm for general functions, but also R-linear convergence for uniformly convex functions is further proved. The numerical performance for both the traditional test functions and image restoration problems show that the proposed algorithm is efficient.

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“…Exploiting the simplicity and low storage requirement of the conjugate gradient method [1,2], in recent times, several authors have extended many conjugate gradient algorithms designed to solve unconstrained optimization problems to solve large-scale nonlinear equations (1.6) (see [3][4][5][6][7][8][9][10][11][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]36]). For instance, using the projection scheme of Solodov and Svaiter [35], Xiao and Zhu [38] extended the Hager and Zhang conjugate descent (CG DESCENT) method to solve (1.6).…”

Section: Introductionmentioning

confidence: 99%

"A descent three-term derivative-free method for signal reconstruction in compressive sensing"

Ibrahim¹,

ABUBAKAR²,

ABUBAKAR³

2022

CJM

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"Many real-world phenomena in engineering, economics, statistical inference, compressed sensing and machine learning involve finding sparse solutions to under-determined or ill-conditioned equations. Our interest in this paper is to introduce a derivative-free method for recovering sparse signal and blurred image arising in compressed sensing by solving a nonlinear equation involving a monotone operator. The global convergence of the proposed method is established under the assumptions of monotonicity and Lipschitz continuity of the underlying operator. Numerical experiments are performed to illustrate the efficiency of the proposed method in the reconstruction of sparse signals and blurred images."

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A Family of Derivative-Free Conjugate Gradient Methods for Constrained Nonlinear Equations and Image Restoration

Cited by 45 publications

References 50 publications

Projection method with inertial step for nonlinear equations: Application to signal recovery

Projection method with inertial step for nonlinear equations: Application to signal recovery

A Dynamically Adjusted Subspace Gradient Method and Its Application in Image Restoration

"A descent three-term derivative-free method for signal reconstruction in compressive sensing"

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