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

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 248 ◽  
Author(s):  
Suthep Suantai ◽  
Pronpat Peeyada ◽  
Damrongsak Yambangwai ◽  
Watcharaporn Cholamjiak
Keyword(s):  
Variational Inequality ◽  
Hilbert Spaces ◽  
Hybrid Algorithm ◽  
Variational Inequality Problems ◽  
Strong Convergence Theorem ◽  
Infinite Dimensional ◽  
Common Solution ◽  
Line Method ◽  
The Common ◽  
Monotone Hybrid Algorithm

In this paper, we study a modified viscosity type subgradient extragradient-line method with a parallel monotone hybrid algorithm for approximating a common solution of variational inequality problems. Under suitable conditions in Hilbert spaces, the strong convergence theorem of the proposed algorithm to such a common solution is proved. We then give numerical examples in both finite and infinite dimensional spaces to justify our main theorem. Finally, we can show that our proposed algorithm is flexible and has good quality for use with common types of blur effects in image recovery.

scholarly journals An Inertial Iterative Algorithm to Find Common Solution of a Split Generalized Equilibrium and a Variational Inequality Problem in Hilbert Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Mohammad Farid ◽  
Rehan Ali ◽  
Watcharaporn Cholamjiak
Keyword(s):  
Variational Inequality ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Variational Inequality Problem ◽  
Field Of Study ◽  
Inequality Problem ◽  
Numerical Example ◽  
Common Solution ◽  
Generalized Equilibrium ◽  
The Common

In this paper, we introduce and study an iterative algorithm via inertial and viscosity techniques to find a common solution of a split generalized equilibrium and a variational inequality problem in Hilbert spaces. Further, we prove that the sequence generated by the proposed theorem converges strongly to the common solution of our problem. Furthermore, we list some consequences of our established algorithm. Finally, we construct a numerical example to demonstrate the applicability of the theorem. We emphasize that the result accounted in the manuscript unifies and extends various results in this field of study.

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 Convergence Theorems for the Variational Inequality Problems and Split Feasibility Problems in Hilbert Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Panisa Lohawech ◽  
Anchalee Kaewcharoen ◽  
Ali Farajzadeh
Keyword(s):  
Variational Inequality ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Iterative Algorithms ◽  
Descent Method ◽  
Variational Inequality Problems ◽  
Steepest Descent Method ◽  
Split Feasibility Problems ◽  
The Common ◽  
Split Feasibility

In this paper, we establish an iterative algorithm by combining Yamada’s hybrid steepest descent method and Wang’s algorithm for finding the common solutions of variational inequality problems and split feasibility problems. The strong convergence of the sequence generated by our suggested iterative algorithm to such a common solution is proved in the setting of Hilbert spaces under some suitable assumptions imposed on the parameters. Moreover, we propose iterative algorithms for finding the common solutions of variational inequality problems and multiple-sets split feasibility problems. Finally, we also give numerical examples for illustrating our algorithms.

scholarly journals A New Hybrid Projection Algorithm for System of Equilibrium Problems and Variational Inequality Problems and Two Finite Families of Quasi-ϕ-Nonexpansive Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Pongrus Phuangphoo ◽  
Poom Kumam
Keyword(s):  
Variational Inequality ◽  
Iterative Procedure ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Variational Inequality Problems ◽  
Projection Algorithm ◽  
Common Solution ◽  
The Common ◽  
System Of Equilibrium Problems

We introduce a modified Mann’s iterative procedure by using the hybrid projection method for solving the common solution of the system of equilibrium problems for a finite family of bifunctions satisfying certain condition, the common solution of fixed point problems for two finite families of quasi-ϕ-nonexpansive mappings, and the common solution of variational inequality problems for a finite family of continuous monotone mappings in a uniformly smooth and strictly convex real Banach space. Then, we prove a strong convergence theorem of the iterative procedure generated by some mild conditions. Our result presented in this paper improves and generalizes some well-known results in the literature.

scholarly journals Viscosity Approximation Methods with Errors and Strong Convergence Theorems for a Common Point of Pseudocontractive and Monotone Mappings: Solutions of Variational Inequality Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Yan Tang
Keyword(s):  
Variational Inequality ◽  
Strong Convergence ◽  
Iterative Algorithms ◽  
Finite Family ◽  
Variational Inequality Problems ◽  
Monotone Mappings ◽  
Convergence Theorems ◽  
Common Solution ◽  
The Common ◽  
Viscosity Approximation Methods

We introduce two proximal iterative algorithms with errors which converge strongly to the common solution of certain variational inequality problems for a finite family of pseudocontractive mappings and a finite family of monotone mappings. The strong convergence theorems are obtained under some mild conditions. Our theorems extend and unify some of the results that have been proposed for this class of nonlinear mappings.

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