scholarly journals On the stability of a dual weak vector variational inequality problem

2008 ◽  
Vol 4 (1) ◽  
pp. 155-165 ◽  
Author(s):  
S. J. Li ◽  
◽  
Z. M. Fang
Keyword(s):  
Variational Inequality ◽  
Variational Inequality Problem ◽  
Vector Variational Inequality ◽  
Inequality Problem ◽  
The Stability ◽  
Vector Variational Inequality Problem ◽  
Weak Vector

The Stability of Solution Set to η-Set-Valued Weak Vector Variational Inequality Problem

2014 ◽  
Vol 668-669 ◽  
pp. 1134-1137
Author(s):  
Jing Jia ◽  
Shui Fang Yin ◽  
Chang Chang Bu
Keyword(s):  
Variational Inequality ◽  
Variational Inequality Problem ◽  
Vector Variational Inequality ◽  
Solution Set ◽  
Inequality Problem ◽  
Stability Of Solution ◽  
The Stability ◽  
Vector Variational Inequality Problem ◽  
Weak Vector

In this paper, we discuss the upper semi-continuity of the solution to parameterη-Set-valued weak vector variational inequality problem. We show that the operator of parameterη-Set-valued weak vector variational inequality is not continuous, but it satisfiesν-semicontinuous andη-weakCpseudo-monotone. Our results generalize the previous results in the literature.

scholarly journals Existence theorems for vector variational inequalities

1996 ◽  
Vol 54 (3) ◽  
pp. 473-481 ◽  
Author(s):  
Aris Daniilidis ◽  
Nicolas Hadjisavvas
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Banach Spaces ◽  
Convex Subset ◽  
Variational Inequality Problem ◽  
Existence Of Solutions ◽  
Existence Theorems ◽  
Multivalued Operator ◽  
Inequality Problem ◽  
Vector Variational Inequality Problem

Given two real Banach spaces X and Y, a closed convex subset K in X, a cone with nonempty interior C in Y and a multivalued operator from K to 2L(x, y), we prove theorems concerning the existence of solutions for the corresponding vector variational inequality problem, that is the existence of some x0 ∈ K such that for every x ∈ K we have A(x − x0) ∉ − int C for some A ∈ Tx0. These results correct previously published ones.

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.

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