Hybrid Algorithms for Variational Inequalities Involving a Strict Pseudocontraction

Cho, Sun Young

doi:10.3390/sym11121502

Cited by 2 publications

(2 citation statements)

References 24 publications

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“…With the help of EM (3), it is possible to construct a sequence in a finite dimensional space that is controlled by the Lipschitz continuity and monotonicity of F, which can then be used to obtain the VIP(F, C) solution in a finite dimensional space using the EM (3) formula for the VIP(F, C) solution. A number of variants of Korpelevich's EM have been examined as a consequence of this starting point, e.g., [5][6][7][8][9][10], as well as the sources cited within [5][6][7][8][9][10] and elsewhere. A few of the researchers who have made significant contributions to this area of study include Censor, Gibali, and Reich [11].…”

Section: Introductionmentioning

confidence: 99%

RETRACTED: Computational Analysis of Variational Inequalities Using Mean Extra-Gradient Approach

Cai

Liu

et al. 2022

Mathematics

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An improved variational inequality strategy for dealing with variational inequality in a Hilbert space is proposed in this article as an alternative; if Hilbert space is used as the domain of interest, the original extra-gradient method is proposed for resolving variational inequality. This improved variational inequality strategy can be used as a substitute for the original extra-gradient method in some situations. Mann’s mean value method, coupled with the widely used sub-gradient extra-gradient strategy, makes it possible to update all of the previous iterations in a single step, thus saving time and effort. All of this is made feasible via the use of Mann’s mean value technique in conjunction with the convex hull of all prior iterations of the algorithm. It is guaranteed that the mean value iteration will result in an acceptable resolution of a variational inequality issue as long as one or more of the criteria for the averaging matrix are fulfilled. Numerous experiments were performed in order to demonstrate the correctness of the theoretical conclusion obtained.

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Section: Introductionmentioning

confidence: 99%

RETRACTED: Computational Analysis of Variational Inequalities Using Mean Extra-Gradient Approach

Cai

Liu

et al. 2022

Mathematics

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show abstract

“…In the setting of a finite dimensional space, it has been proved that the sequence generated by EM (3) converges to a solution of VIP(F, C) governed by Lipschitz continuity and monotonicity of F. From such starting point, several variants of Korpelevich's EM have been investigated, for instance [4][5][6][7][8][9] and references there cited in. Especially, we only underline here the work of Censor, Gibali and Reich [10].…”

Section: Introductionmentioning

confidence: 99%

A Mean Extragradient Method for Solving Variational Inequalities

2021

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We propose a modified extragradient method for solving the variational inequality problem in a Hilbert space. The method is a combination of the well-known subgradient extragradient with the Mann’s mean value method in which the updated iterate is picked in the convex hull of all previous iterates. We show weak convergence of the mean value iterate to a solution of the variational inequality problem, provided that a condition on the corresponding averaging matrix is fulfilled. Some numerical experiments are given to show the effectiveness of the obtained theoretical result.

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Hybrid Algorithms for Variational Inequalities Involving a Strict Pseudocontraction

Cited by 2 publications

References 24 publications

RETRACTED: Computational Analysis of Variational Inequalities Using Mean Extra-Gradient Approach

RETRACTED: Computational Analysis of Variational Inequalities Using Mean Extra-Gradient Approach

A Mean Extragradient Method for Solving Variational Inequalities

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