On the finite dimensional approximations of some mixed variational inequalities

2015 ◽  
Vol 9 ◽  
pp. 5697-5705 ◽  
Author(s):  
I.B. Badriev ◽  
V.V. Banderov ◽  
V.L. Gnedenkova ◽  
N.V. Kalacheva ◽  
A.I. Korablev ◽  
...  
Keyword(s):  
Variational Inequalities ◽  
Finite Dimensional ◽  
Mixed Variational Inequalities

scholarly journals An Interior Projected-Like Subgradient Method for Mixed Variational Inequalities

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Guo-ji Tang ◽  
Xing Wang
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Subgradient Method ◽  
Mixed Variational Inequality ◽  
Convergence Estimate ◽  
Finite Dimensional ◽  
Mixed Variational Inequalities

An interior projected-like subgradient method for mixed variational inequalities is proposed in finite dimensional spaces, which is based on using non-Euclidean projection-like operator. Under suitable assumptions, we prove that the sequence generated by the proposed method converges to a solution of the mixed variational inequality. Moreover, we give the convergence estimate of the method. The results presented in this paper generalize some recent results given in the literatures.

Differential mixed variational inequalities in finite dimensional spaces

2010 ◽  
Vol 72 (9-10) ◽  
pp. 3875-3886 ◽  
Author(s):  
Xue-song Li ◽  
Nan-jing Huang ◽  
Donal O’Regan
Keyword(s):  
Variational Inequalities ◽  
Finite Dimensional ◽  
Mixed Variational Inequalities

scholarly journals Well-posedness by perturbations of variational-hemivariational inequalities with perturbations

Filomat ◽  
2012 ◽  
Vol 26 (5) ◽  
pp. 881-895 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Himanshu Gupta ◽  
Ching-Feng Wen
Keyword(s):  
Variational Inequalities ◽  
Hemivariational Inequality ◽  
Inclusion Problem ◽  
Hemivariational Inequalities ◽  
Well Posedness ◽  
Mild Conditions ◽  
Finite Dimensional ◽  
Mixed Variational Inequalities ◽  
Well Posed ◽  
Special Case

In this paper, we consider an extension of the notion of well-posedness by perturbations, introduced by Zolezzi for a minimization problem, to a class of variational-hemivariational inequalities with perturbations in Banach spaces, which includes as a special case the class of mixed variational inequalities. Under very mild conditions, we establish some metric characterizations for the well-posed variational-hemivariational inequality, and show that the well-posedness by perturbations of a variational-hemivariational inequality is closely related to the well-posedness by perturbations of the corresponding inclusion problem. Furthermore, in the setting of finite-dimensional spaces we also derive some conditions under which the variational-hemivariational inequality is strongly generalized well-posed-like by perturbations.

scholarly journals Some Proximal Methods for Solving Mixed Variational Inequalities

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Muhammad Aslam Noor ◽  
Zhenyu Huang
Keyword(s):  
Variational Inequalities ◽  
Extragradient Method ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Proximal Methods ◽  
Proximal Point ◽  
Equivalent Formulation ◽  
New Methods ◽  
Special Cases ◽  
Mixed Variational Inequalities

It is well known that the mixed variational inequalities are equivalent to the fixed point problem. We use this alternative equivalent formulation to suggest some new proximal point methods for solving the mixed variational inequalities. These new methods include the explicit, the implicit, and the extragradient method as special cases. The convergence analysis of these new methods is considered under some suitable conditions. Our method of constructing these iterative methods is very simple. Results proved in this paper may stimulate further research in this direction.

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