scholarly journals Accelerated Modified Tseng’s Extragradient Method for Solving Variational Inequality Problems in Hilbert Spaces

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 248
Author(s):  
Godwin Amechi Okeke ◽  
Mujahid Abbas ◽  
Manuel De la Sen ◽  
Hira Iqbal
Keyword(s):  
Variational Inequality ◽  
Hilbert Spaces ◽  
Variational Inequality Problem ◽  
Extragradient Method ◽  
Convergence Result ◽  
Variational Inequality Problems ◽  
Numerical Examples ◽  
Mild Conditions ◽  
Tseng’S Extragradient Method ◽  
Better Than

The aim of this paper is to propose a new iterative algorithm to approximate the solution for a variational inequality problem in real Hilbert spaces. A strong convergence result for the above problem is established under certain mild conditions. Our proposed method requires the computation of only one projection onto the feasible set in each iteration. Some numerical examples are presented to support that our proposed method performs better than some known comparable methods for solving variational inequality problems.

A new self adaptive Tseng’s extragradient method with double-projection for solving pseudomonotone variational inequality problems in Hilbert spaces

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Zhongbing Xie ◽  
Gang Cai ◽  
Xiaoxiao Li ◽  
Qiao-Li Dong
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Convergence Theorem ◽  
Numerical Experiments ◽  
Extragradient Method ◽  
Variational Inequality Problems ◽  
Strong Convergence Theorem ◽  
Tseng’S Extragradient Method

Abstract The purpose of this paper is to study a new Tseng’s extragradient method with two different stepsize rules for solving pseudomonotone variational inequalities in real Hilbert spaces. We prove a strong convergence theorem of the proposed algorithm under some suitable conditions imposed on the parameters. Moreover, we also give some numerical experiments to demonstrate the performance of our algorithm.

scholarly journals A Generalized Strong Convergence Algorithm in the Presence of Errors for Variational Inequality Problems in Hilbert Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Mostafa Ghadampour ◽  
Donal O’Regan ◽  
Ebrahim Soori ◽  
Ravi P. Agarwal
Keyword(s):  
Variational Inequality ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Variational Inequality Problem ◽  
Numerical Algorithms ◽  
Variational Inequality Problems ◽  
Numerical Examples ◽  
Inequality Problem ◽  
Convergence Of An Algorithm ◽  
Computational Errors

In this paper, we study the strong convergence of an algorithm to solve the variational inequality problem which extends a recent paper (Thong et al., Numerical Algorithms. 78, 1045-1060 (2018)). We reduce and refine some of their algorithm conditions and we prove the convergence of the algorithm in the presence of some computational errors. Then, using the MATLAB software, the result will be illustrated with some numerical examples. Also, we compare our algorithm with some other well-known algorithms.

scholarly journals Inertial Extra-Gradient Method for Solving a Family of Strongly Pseudomonotone Equilibrium Problems in Real Hilbert Spaces with Application in Variational Inequality Problem

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 503 ◽  
Author(s):  
Habib ur Rehman ◽  
Poom Kumam ◽  
Ioannis K. Argyros ◽  
Wejdan Deebani ◽  
Wiyada Kumam
Keyword(s):  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Variational Inequality Problem ◽  
Extragradient Method ◽  
Convergence Result ◽  
Iterative Sequence ◽  
Type Condition ◽  
Mild Conditions ◽  
Slow Moving ◽  
Set Up

In this paper, we propose a new method, which is set up by incorporating an inertial step with the extragradient method for solving a strongly pseudomonotone equilibrium problems. This method had to comply with a strongly pseudomonotone property and a certain Lipschitz-type condition of a bifunction. A strong convergence result is provided under some mild conditions, and an iterative sequence is accomplished without previous knowledge of the Lipschitz-type constants of a cost bifunction. A sufficient explanation is that the method operates with a slow-moving stepsize sequence that converges to zero and non-summable. For numerical explanations, we analyze a well-known equilibrium model to support our well-established convergence result, and we can see that the proposed method seems to have a significant consistent improvement over the performance of the existing methods.

scholarly journals Inertial S-type Tseng's extragradient Algorithm for solution of Variational Inequality problems

2021 ◽  
Author(s):  
D. R. Sahu ◽  
AMIT KUMAR SINGH
Keyword(s):  
Variational Inequality ◽  
Hilbert Spaces ◽  
Iteration Process ◽  
Variational Inequality Problems ◽  
Numerical Examples ◽  
Lipschitz Continuous ◽  
Mild Conditions ◽  
Extragradient Algorithm ◽  
Convergence Results ◽  
Continuous Operators

In this paper, we introduce inertial Tseng’s extragradient algorithms combined with normal-S iteration process for solving variational inequality problems involving pseudo-monotone and Lipschitz continuous operators. Under mild conditions, we establish the weak convergence results in Hilbert spaces. Numerical examples are also present to show that faster behaviour of the proposed method.

scholarly journals Inertial Optimization Based Two-Step Methods for Solving Equilibrium Problems with Applications in Variational Inequality Problems and Growth Control Equilibrium Models

Energies ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 3292 ◽  
Author(s):  
Habib ur Rehman ◽  
Poom Kumam ◽  
Meshal Shutaywi ◽  
Nasser Aedh Alreshidi ◽  
Wiyada Kumam
Keyword(s):  
Variational Inequality ◽  
Equilibrium Problems ◽  
Extragradient Method ◽  
Mathematical Finance ◽  
Convergence Result ◽  
Variational Inequality Problems ◽  
Subgradient Extragradient Method ◽  
Pseudomonotone Operator ◽  
Equilibrium Models ◽  
Variable Stepsize

This manuscript aims to incorporate an inertial scheme with Popov’s subgradient extragradient method to solve equilibrium problems that involve two different classes of bifunction. The novelty of our paper is that methods can also be used to solve problems in many fields, such as economics, mathematical finance, image reconstruction, transport, elasticity, networking, and optimization. We have established a weak convergence result based on the assumption of the pseudomonotone property and a certain Lipschitz-type cost bifunctional condition. The stepsize, in this case, depends upon on the Lipschitz-type constants and the extrapolation factor. The bifunction is strongly pseudomonotone in the second method, but stepsize does not depend on the strongly pseudomonotone and Lipschitz-type constants. In contrast, the first convergence result, we set up strong convergence with the use of a variable stepsize sequence, which is decreasing and non-summable. As the application, the variational inequality problems that involve pseudomonotone and strongly pseudomonotone operator are considered. Finally, two well-known Nash–Cournot equilibrium models for the numerical experiment are reviewed to examine our convergence results and show the competitive advantage of our suggested methods.

scholarly journals An Iterative Method for a Common Solution of a Combination of the Split Equilibrium Problem, a Finite Family of Nonexpansive Mapping and a Combination of Variational Inequality Problem

2021 ◽  
Vol 52 ◽  
Author(s):  
Ihssane Hay ◽  
Abdellah Bnouhachem ◽  
Themistocles M. Rassias
Keyword(s):  
Variational Inequality ◽  
Iterative Method ◽  
Equilibrium Problem ◽  
Hilbert Spaces ◽  
Variational Inequality Problem ◽  
Convergence Result ◽  
Finite Family ◽  
Split Equilibrium Problem ◽  
Inequality Problem ◽  
Common Solution

The present paper aims to deal with an iterative algorithm for finding common solution of the combination of the split equilibrium problem and a finite family of non-expansive mappings and the combination of variational inequality problem in the setting of real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution to these problems. A numerical example is presented to illustrate the proposed method and convergence result. The results and method presented in this paper generalize, extend and unify some known results in the literatures.

scholarly journals Analysis of Subgradient Extragradient Iterative Schemes for Variational Inequalities

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Danfeng Wu ◽  
Li-Jun Zhu ◽  
Zhuang Shan ◽  
Tzu-Chien Yin
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Convergence Analysis ◽  
Hilbert Spaces ◽  
Extragradient Method ◽  
Subgradient Extragradient Method ◽  
Iterative Schemes ◽  
Mild Conditions ◽  
Monotone Variational Inequality

In this paper, we investigate the monotone variational inequality in Hilbert spaces. Based on Censor’s subgradient extragradient method, we propose two modified subgradient extragradient algorithms with self-adaptive and inertial techniques for finding the solution of the monotone variational inequality in real Hilbert spaces. Strong convergence analysis of the proposed algorithms have been obtained under some mild conditions.

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