An extended inertial Halpern-type ball-relaxed CQ algorithm for multiple-sets split feasibility problem

Taddele, Guash Haile; Berinde, Vasile

doi:10.1007/s43034-022-00190-9

Cited by 4 publications

(2 citation statements)

References 46 publications

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“…As a result, improving image quality, which is the aim of image restoration, is worth contemplating. For related topics in this work, see [16,31,33], and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Modified inertial subgradient extragradient with auxiliary parameters and parallel viscosity algorithm for minimization problem induced by bounded linear operator over common solution of fixed points of nonexpansive mappings and pseudomonotone equilibrium problems

Khonchaliew,

Khamdam,

Petrot

et al. 2024

J. Math. Computer Sci.

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This paper introduces a modification to the inertial subgradient extragradient algorithm by incorporating auxiliary parameters for updating, along with dynamic regularization coefficient, including the parallel viscosity algorithm. The aim is to find an element in the common solution set of fixed points in a finite family of nonexpansive mappings and Lipschitz-type continuous pseudomonotone equilibrium problems. This element also serves as the unique solution to a minimization problem induced by a bounded linear operator and contraction mapping in the context of a real Hilbert space. The efficiency of the proposed algorithm is influenced by the introduced auxiliary parameters, which are intended to leverage the value of the considered objective bifunction at each iteration, along with the advantages of the designed regularization coefficient, which is self-adaptive and utilizes a straightforward rule for automatic updates. The update rule avoids enforcing monotonic behavior on the dynamic regularization coefficient and does not require prior knowledge of the Lipschitz constants of the bifunction. This flexibility increases the algorithm's applicability for solving a wider range of practical problems. The discussions on the numerical experiments for Nash-Cournot models and image restoration problems are also provided to illustrate the computational effectiveness of the introduced algorithm.

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“…As a result, improving image quality, which is the aim of image restoration, is worth contemplating. For related topics in this work, see [16,31,33], and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Modified inertial subgradient extragradient with auxiliary parameters and parallel viscosity algorithm for minimization problem induced by bounded linear operator over common solution of fixed points of nonexpansive mappings and pseudomonotone equilibrium problems

Khonchaliew,

Khamdam,

Petrot

et al. 2024

J. Math. Computer Sci.

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“…But the convergence rate of the Mann algorithm is slow in general. Due to the fact that fast convergence is required in many practical applications (see, [8,16,17,27]), many researchers constructed fast iterative algorithms by using inertial extrapolation methods (see [1,5,7,9,20,[32][33][34]). Specifically, Mainge [22] developed the following algorithm by employing the Mann algorithm together with inertial extrapolation method:…”

Section: Introductionmentioning

confidence: 99%

Convergence Results on the General Inertial-Mann-Halpern and General Inertial Mann Algorithms

Gebregiorgis

2023

Preprint

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In this paper, we prove strong convergence theorem of the general inertial Mann-Halpern algorithm for nonexpansive mappings in the setting of Hilbert spaces.we also prove weak convergence theorem of the general inertial Mann algorithmfor k-strict pseudo-contractive mappings in the setting of Hilbert spaces. These convergence results extend and generalize some existing results in the literature.Finally, we provide examples to verify our main results.

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Multi-step inertial algorithms for equilibrium, fixed point, general systems of variational inequalities and split feasibility problems

Li,

He,

Wang

2024

Indian J Pure Appl Math

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An extended inertial Halpern-type ball-relaxed CQ algorithm for multiple-sets split feasibility problem

Cited by 4 publications

References 46 publications

Modified inertial subgradient extragradient with auxiliary parameters and parallel viscosity algorithm for minimization problem induced by bounded linear operator over common solution of fixed points of nonexpansive mappings and pseudomonotone equilibrium problems

Modified inertial subgradient extragradient with auxiliary parameters and parallel viscosity algorithm for minimization problem induced by bounded linear operator over common solution of fixed points of nonexpansive mappings and pseudomonotone equilibrium problems

Convergence Results on the General Inertial-Mann-Halpern and General Inertial Mann Algorithms

Multi-step inertial algorithms for equilibrium, fixed point, general systems of variational inequalities and split feasibility problems

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