Accelerated preconditioning Krasnosel'skiĭ-Mann method for efficiently solving monotone inclusion problems

Artsawang, Natthaphon

doi:10.3934/math.20231453

MATH

2023

DOI: 10.3934/math.20231453

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Accelerated preconditioning Krasnosel'skiĭ-Mann method for efficiently solving monotone inclusion problems

Natthaphon Artsawang

Abstract: <abstract>In this article, we propose a strongly convergent preconditioning method for finding a zero of the sum of two monotone operators. The proposed method combines a preconditioning approach with the robustness of the Krasnosel'skiĭ-Mann method. We show the strong convergence result of the sequence generated by the proposed method to a solution of the monotone inclusion problem. Finally, we provide numerical experiments on the convex minimization problem.</abstract>

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Cited by 3 publications

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Double Tseng’s Algorithm with Inertial Terms for Inclusion Problems and Applications in Image Deblurring

Thammasiri,

Berinde,

Petrot

et al. 2024

Mathematics

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In this research paper, we present a novel theoretical technique, referred to as the double Tseng’s algorithm with inertial terms, for finding a common solution to two monotone inclusion problems. Developing the double Tseng’s algorithm in this manner not only comprehensively expands theoretical knowledge in this field but also provides advantages in terms of step-size parameters, which are beneficial for tuning applications and positively impact the numerical results. This new technique can be effectively applied to solve the problem of image deblurring and offers numerical advantages compared to some previously related results. By utilizing certain properties of a Lipschitz monotone operator and a maximally monotone operator, along with the identity associated with the convexity of the quadratic norm in the framework of Hilbert spaces, and by imposing some constraints on the scalar control conditions, we can achieve weak convergence to a common zero point of the sum of two monotone operators. To demonstrate the benefits and advantages of this newly proposed algorithm, we performed numerical experiments to measure the improvement in the signal–to–noise ratio (ISNR) and the structural similarity index measure (SSIM). The results of both numerical experiments (ISNR and SSIM) demonstrate that our new algorithm is more efficient and has a significant advantage over the relevant preceding algorithms.

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Double Tseng’s Algorithm with Inertial Terms for Inclusion Problems and Applications in Image Deblurring

Thammasiri,

Berinde,

Petrot

et al. 2024

Mathematics

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A generalized viscosity forward-backward splitting scheme with inertial terms for solving monotone inclusion problems and its applications

Ungchittrakool,

Artsawang

2024

MATH

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Our aim was to establish a novel generalized viscosity forward-backward splitting scheme that incorporates inertial terms for addressing monotone inclusion problems within a Hilbert space. By incorporating appropriate control conditions, we achieved strong convergence. The significance of this theorem lies in its applicability to resolve convex minimization problems. To demonstrate the efficacy of our proposed algorithm, we conducted a comparative analysis of its convergence behavior against other algorithms. Finally, we showcased the performance of our proposed method through numerical experiments aimed at addressing image restoration problems.

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Nonmonotone variable metric Barzilai-Borwein method for composite minimization problem

Guo,

Xu,

Zhu

et al. 2024

MATH

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<abstract>In this study, we develop a nonmonotone variable metric Barzilai-Borwein method for minimizing the sum of a smooth function and a convex, possibly nondifferentiable, function. At each step, the descent direction is obtained by taking the difference between the minimizer of the scaling proximal function and the current iteration point. An adaptive nonmonotone line search is proposed for determining the step length along this direction. We also show that the limit point of the iterates sequence is a stationary point. Numerical results with parallel magnetic resonance imaging, Poisson, and Cauchy noise deblurring demonstrate the effectiveness of the new algorithm.</abstract>

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Accelerated preconditioning Krasnosel'skiĭ-Mann method for efficiently solving monotone inclusion problems

Cited by 3 publications

References 26 publications

Double Tseng’s Algorithm with Inertial Terms for Inclusion Problems and Applications in Image Deblurring

Double Tseng’s Algorithm with Inertial Terms for Inclusion Problems and Applications in Image Deblurring

A generalized viscosity forward-backward splitting scheme with inertial terms for solving monotone inclusion problems and its applications

Nonmonotone variable metric Barzilai-Borwein method for composite minimization problem

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