A modified conjugate gradient algorithm with backtracking line search technique for large-scale nonlinear equations

Li, Xiangrong; Wang, Xiaoliang; Zhou, Sheng; Duan, Xiabin

doi:10.1080/00207160.2017.1290433

“…From (17), we arrived at (18) which show that the direction is bounded. The next theorem is proved by contradiction, and the boundedness of the direction is required to establish the contradiction in (22).…”

Section: Algorithm 1 (Mcdpm)mentioning

confidence: 97%

Two Hybrid Spectral Methods With Inertial Effect for Solving System of Nonlinear Monotone Equations With Application in Robotics

Aji

¹

,

Awwal

²

,

Yahaya

³

et al. 2021

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In this paper, we propose a modified conjugate descent (CD) projection algorithm for solving system of nonlinear monotone equations with convex constraints. The search direction in this algorithm use a convex combination of the steepest descent algorithm and the well-known CD method. The algorithm proves to be quite efficient for solving large scale monotone nonlinear equations, as it has low storage requirement and does not need the computation of Jacobian matrix. We prove the convergence of the algorithm using some conditions, and perform numerical experiments on some test problems. In order to show the efficiency of our proposed algorithm, the numerical performance is compared with some existing algorithms. Finally, by reformulating 1 regularized problem into monotone equation, we successfully apply the algorithm to restore some blurred images. The numerical results obtained prove that the algorithm can be used as an efficient and qualitative solver for image restoration problems.

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“…From (17), we arrived at (18) which show that the direction is bounded. The next theorem is proved by contradiction, and the boundedness of the direction is required to establish the contradiction in (22).…”

Section: Algorithm 1 (Mcdpm)mentioning

confidence: 97%

A Modified Conjugate Descent Projection Method for Monotone Nonlinear Equations and Image Restoration

Aji

¹

,

Siricharoen

²

,

Abubakar

³

et al. 2020

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In this paper, we propose a modified conjugate descent (CD) projection algorithm for solving system of nonlinear monotone equations with convex constraints. The search direction in this algorithm use a convex combination of the steepest descent algorithm and the well-known CD method. The algorithm proves to be quite efficient for solving large scale monotone nonlinear equations, as it has low storage requirement and does not need the computation of Jacobian matrix. We prove the convergence of the algorithm using some conditions, and perform numerical experiments on some test problems. In order to show the efficiency of our proposed algorithm, the numerical performance is compared with some existing algorithms. Finally, by reformulating 1 regularized problem into monotone equation, we successfully apply the algorithm to restore some blurred images. The numerical results obtained prove that the algorithm can be used as an efficient and qualitative solver for image restoration problems.

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“…Li and Li [22] introduced a derivative-free three-term PRP method for solving nonlinear systems of monotone equations. You can also find further derivative-free type methods in [23][24][25][26][27] etc.…”

Section: Introductionmentioning

confidence: 99%

A projection method for solving monotone nonlinear equations with application

Abbass,

Chen,

Abdullahi

et al. 2023

Phys. Scr.

1

0

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Nonlinear equations are one of the most trending research areas due to their vast applications in the field of sciences, social sciences, and engineering. However, the conjugate gradient method (CG) is the most effective and rapidly developing iterative technique for solving nonlinear monotone problems. Recently, much work has been done on using the CG method to solve monotone nonlinear equations. This paper discusses a new variant for solving constrained monotone nonlinear equations. The method satisfies the sufficient descent condition and proves global convergence with the help of some reasonable assumptions. Two sets of numerical tests were conducted. The first experiment shows the good performance of the proposed method compared to existing methods, while the second experiment displays the performance of motion control of two-joint planar robot manipulator.

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A modified conjugate gradient algorithm with backtracking line search technique for large-scale nonlinear equations

Cited by 10 publications

References 41 publications

Two Hybrid Spectral Methods With Inertial Effect for Solving System of Nonlinear Monotone Equations With Application in Robotics

Two Hybrid Spectral Methods With Inertial Effect for Solving System of Nonlinear Monotone Equations With Application in Robotics

A Modified Conjugate Descent Projection Method for Monotone Nonlinear Equations and Image Restoration

A projection method for solving monotone nonlinear equations with application

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