Regularization methods for certain quasi-variational inequalities with inexactly given data in a Hilbert space

2007 ◽  
Vol 47 (8) ◽  
pp. 1232-1242
Author(s):  
I. P. Ryazantseva
Keyword(s):  
Hilbert Space ◽  
Variational Inequalities ◽  
Regularization Methods

scholarly journals On Iterative Regularization Methods for Variational Inequalities of the Second Kind with Pseudomonotone Operators

2003 ◽  
Vol 3 (2) ◽  
pp. 223-234 ◽  
Author(s):  
I. B. Badriev ◽  
O. A. Zadvornov ◽  
L. N. Ismagilov
Keyword(s):  
Hilbert Space ◽  
Iterative Method ◽  
Variational Inequalities ◽  
Regularization Methods ◽  
Pseudomonotone Operators ◽  
Iterative Regularization ◽  
Implicit Iterative Method

Abstract Variational inequalitiy of the second kind in the Banach or Hilbert space is considered. A ”semi-implicit” iterative method for its solution is studied.

scholarly journals Hybrid Projection Algorithm for a New General System of Variational Inequalities in Hilbert Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-22
Author(s):  
S. Imnang
Keyword(s):  
Hilbert Space ◽  
Variational Inequalities ◽  
Nonexpansive Mapping ◽  
Real Hilbert Space ◽  
General System ◽  
Projection Algorithm ◽  
Common Element ◽  
System Of Variational Inequalities ◽  
Demiclosedness Principle ◽  
Hybrid Projection Algorithm

A new general system of variational inequalities in a real Hilbert space is introduced and studied. The solution of this system is shown to be a fixed point of a nonexpansive mapping. We also introduce a hybrid projection algorithm for finding a common element of the set of solutions of a new general system of variational inequalities, the set of solutions of a mixed equilibrium problem, and the set of fixed points of a nonexpansive mapping in a real Hilbert space. Several strong convergence theorems of the proposed hybrid projection algorithm are established by using the demiclosedness principle. Our results extend and improve recent results announced by many others.

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.

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