A Parallel-Viscosity-Type Subgradient Extragradient-Line Method for Finding the Common Solution of Variational Inequality Problems Applied to Image Restoration Problems

Suantai, Suthep; Peeyada, Pronpat; Yambangwai, Damrongsak; Cholamjiak, Watcharaporn

doi:10.3390/math8020248

Cited by 14 publications

(11 citation statements)

References 34 publications

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“…5. Finally, we compare our main algorithms with PVTSE [29] Figure 7 Cauchy error plots of PVTSE, MHPSE, and the proposed algorithms in all cases of RGB images and MHPSE [17] algorithms. It is remarkable that our proposed algorithm has a better convergence rate; see Figs.…”

Section: Discussionmentioning

confidence: 99%

“…Both theoretical and experimental results demonstrate the convergence properties of the proposed algorithm in this section. However, for showing the effectiveness of the proposed algorithm, the PVTSE [29] and MHPSE [17] algorithms are also applied to compare.…”

Section: Application To Image Restoration Problemsmentioning

confidence: 99%

“…Very recently, the parallel method was used to solve common problems in many improved algorithms. One of such is a parallel viscosity-type subgradient extragradient algorithm (PVTSE) introduced by Suantai et al [29] for solving common variational inequalities. In this work, PVTSE algorithm was applied for solving image recovery problems with common types of blur effects.…”

Section: Introductionmentioning

confidence: 99%

“…A weak convergence theorem is established under some suitable conditions imposed on the bifunction ψ i . In the last section, we apply our algorithms for solving unconstrained image recovery problems and compare our main algorithms with PVTSE [29] and MHPSE [17] algorithms. It is remarkable that our method has a better convergence rate.…”

Section: Introductionmentioning

confidence: 99%

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Solving common nonmonotone equilibrium problems using an inertial parallel hybrid algorithm with Armijo line search with applications to image recovery

2021

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In this work, we modify the inertial hybrid algorithm with Armijo line search using a parallel method to approximate a common solution of nonmonotone equilibrium problems in Hilbert spaces. A weak convergence theorem is proved under some continuity and convexity assumptions on the bifunction and the nonemptiness of the common solution set of Minty equilibrium problems. Furthermore, we demonstrate the quality of our inertial parallel hybrid algorithm by using image restoration, as well as its superior efficiency when compared with previously considered parallel algorithms.

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Section: Discussionmentioning

confidence: 99%

Section: Application To Image Restoration Problemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Solving common nonmonotone equilibrium problems using an inertial parallel hybrid algorithm with Armijo line search with applications to image recovery

2021

Self Cite

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“…If N = 1, CSVIP (5) becomes VIP (1). Very recently, using a modified viscosity-type subgradient extragradient-line method, Suantai et al [19] introduced the parallel viscosity-type subgradient extragradient-line method (PVSEGM) for solving the VIP. The strong convergence theorem was proved when each of the operator A i is Lipschitz continuous monotone mapping that the Lipschitz constant is unknow.…”

Section: Introduction and Definitionsmentioning

confidence: 99%

Image deblurring using a projective inertial parallel subgradient extragradient-line algorithm of variational inequality problems

Suantai

Peeyada

Cholamjiak

et al. 2022

Filomat

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In this paper, we introduce projective inertial parallel subgradient extragradient-line algorithm for solving variational inequalites of L-Lipschitz continuous and monotone mappings which L is unknown. We prove a strong convergence result under some mild conditions in Hilbert space. We also present some numerical examples in Euclidean space R3 compared with Parallel-Viscosity-Type Subgradient Extragradient-Line Method. Finally, we deblur the Grey and RGB images from common types of blur matrixes Gaussian blur, Out of focus blur and Motion blur using our proposed algorithm and show the better efficeincy when the number of types of blur matrixes is large.

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Strong Convergent Inertial Two-subgradient Extragradient Method for Finding Minimum-norm Solutions of Variational Inequality Problems

Opeyemi Alakoya,

Temitope Mewomo

2024

Netw Spat Econ

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In 2012, Censor et al. (Extensions of Korpelevich’s extragradient method for the variational inequality problem in Euclidean space. Optimization 61(9):1119–1132, 2012b) proposed the two-subgradient extragradient method (TSEGM). This method does not require computing projection onto the feasible (closed and convex) set, but rather the two projections are made onto some half-space. However, the convergence of the TSEGM was puzzling and hence posted as open question. Very recently, some authors were able to provide a partial answer to the open question by establishing weak convergence result for the TSEGM though under some stringent conditions. In this paper, we propose and study an inertial two-subgradient extragradient method (ITSEGM) for solving monotone variational inequality problems (VIPs). Under more relaxed conditions than the existing results in the literature, we prove that proposed method converges strongly to a minimum-norm solution of monotone VIPs in Hilbert spaces. Unlike several of the existing methods in the literature for solving VIPs, our method does not require any linesearch technique, which could be time-consuming to implement. Rather, we employ a simple but very efficient self-adaptive step size method that generates a non-monotonic sequence of step sizes. Moreover, we present several numerical experiments to demonstrate the efficiency of our proposed method in comparison with related results in the literature. Finally, we apply our result to image restoration problem. Our result in this paper improves and generalizes several of the existing results in the literature in this direction.

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A Parallel-Viscosity-Type Subgradient Extragradient-Line Method for Finding the Common Solution of Variational Inequality Problems Applied to Image Restoration Problems

Cited by 14 publications

References 34 publications

Solving common nonmonotone equilibrium problems using an inertial parallel hybrid algorithm with Armijo line search with applications to image recovery

Solving common nonmonotone equilibrium problems using an inertial parallel hybrid algorithm with Armijo line search with applications to image recovery

Image deblurring using a projective inertial parallel subgradient extragradient-line algorithm of variational inequality problems

Strong Convergent Inertial Two-subgradient Extragradient Method for Finding Minimum-norm Solutions of Variational Inequality Problems

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