scholarly journals An iterative solution of a variational inequality for certain monotone operators in Hilbert space

1975 ◽  
Vol 81 (5) ◽  
pp. 890-893 ◽  
Author(s):  
Ronald E. Bruck Jr.
Keyword(s):  
Hilbert Space ◽  
Variational Inequality ◽  
Monotone Operators ◽  
Iterative Solution

scholarly journals An iterative regularization method for variational inequalities in Hilbert spaces

2020 ◽  
Vol 36 (3) ◽  
pp. 475-482
Author(s):  
HONG-KUN XU ◽  
NAJLA ALTWAIJRY ◽  
SOUHAIL CHEBBI
Keyword(s):  
Hilbert Space ◽  
Variational Inequality ◽  
Hilbert Spaces ◽  
Regularization Method ◽  
Iterative Solution ◽  
Iterative Regularization ◽  
Lipschitz Continuous ◽  
Ill Posed ◽  
Feasible Solutions ◽  
First Time

We consider an iterative method for regularization of a variational inequality (VI) defined by a Lipschitz continuous monotone operator in the case where the set of feasible solutions is decomposed to the intersection of finitely many closed convex subsets of a Hilbert space. We prove the strong convergence of the sequence generated by our algorithm. It seems that this is the first time in the literature to handle iterative solution of ill-posed VIs in the domain decomposition case.

scholarly journals New Tseng-Degree Gradient Method in Variational Inequality Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Zhuang Shan ◽  
Lijun Zhu ◽  
Long He ◽  
Danfeng Wu ◽  
Haicheng Wei
Keyword(s):  
Hilbert Space ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
High Precision ◽  
Gradient Method ◽  
Variational Inequality Problem ◽  
Real Hilbert Space ◽  
Monotone Operators ◽  
Inequality Problem ◽  
Convergence Performance

This paper focuses on the problem of variational inequalities with monotone operators in real Hilbert space. The Tseng algorithm constructed by Thong replaced a high-precision step. Thus, a new Tseng-like gradient method is constructed, and the convergence of the algorithm is proved, and the convergence performance is higher.

scholarly journals Topological degree and application to a parabolic variational inequality problem

2001 ◽  
Vol 25 (4) ◽  
pp. 273-287 ◽  
Author(s):  
A. Addou ◽  
B. Mermri
Keyword(s):  
Variational Inequality ◽  
Topological Degree ◽  
Variational Inequality Problem ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Parabolic Variational Inequality ◽  
Inequality Problem ◽  
Monotone Map ◽  
New Formulation

We are interested in constructing a topological degree for operators of the formF=L+A+S, whereLis a linear densely defined maximal monotone map,Ais a bounded maximal monotone operators, andSis a bounded demicontinuous map of class(S+)with respect to the domain ofL. By means of this topological degree we prove an existence result that will be applied to give a new formulation of a parabolic variational inequality problem.

scholarly journals A Mean Extragradient Method for Solving Variational Inequalities

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 462
Author(s):  
Apichit Buakird ◽  
Nimit Nimana ◽  
Narin Petrot
Keyword(s):  
Hilbert Space ◽  
Variational Inequality ◽  
Weak Convergence ◽  
Numerical Experiments ◽  
Variational Inequality Problem ◽  
Extragradient Method ◽  
Mean Value ◽  
Inequality Problem ◽  
The Mean ◽  
Mean Value Method

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.

scholarly journals New algorithm method for solving the variational inequality problem in Hilbert space

2019 ◽  
Vol 7 (2) ◽  
pp. 15 ◽  
Author(s):  
Zena Hussein Maibed
Keyword(s):  
Hilbert Space ◽  
Variational Inequality ◽  
Variational Inequality Problem ◽  
Inequality Problem ◽  
Resolvent Mappings

Theipurpose of,thisipaper,is toiintroduce,aiconcept of generalizedinon_spreading,and define a new algorithm,for infinite,families of generalizedinon_spreading,and finite families of resolvent,mappings. Also, We study,the existence,solution of variational inequality,to a commonifixedipoint in Hilbertispaces. The main,results in this paper extendiand generalized,of many knowniresults initheiliterature.  

scholarly journals Hybrid Algorithms for Variational Inequalities Involving a Strict Pseudocontraction

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1502
Author(s):  
Sun Young Cho
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Variational Inequality Problem ◽  
Real Hilbert Space ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Strict Pseudocontraction ◽  
Adaptive Step

In a real Hilbert space, we investigate the Tseng’s extragradient algorithms with hybrid adaptive step-sizes for treating a Lipschitzian pseudomonotone variational inequality problem and a strict pseudocontraction fixed-point problem, which are symmetry. By imposing some appropriate weak assumptions on parameters, we obtain a norm solution of the problems, which solves a certain hierarchical variational inequality.

scholarly journals Zeros of Nonlinear Monotone Operators in Hilbert Space*

1978 ◽  
Vol 21 (2) ◽  
pp. 213-219 ◽  
Author(s):  
R. Schöneberg
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Monotone Operators ◽  
Russian Mathematician ◽  
Image Position

Around 1960, the Russian mathematician Kachurovski [1] introduced the notion of monotone operators in Hilbert spaces: Let E be a Hilbert space and X ⊂ E. An operator T:X→E is said to be monotone, iff.

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