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.

scholarly journals On the Hadamard Well-Posedness of Generalized Mixed Variational Inequalities in Banach Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Lu-Chuan Ceng ◽  
Yeong-Cheng Liou ◽  
Ching-Feng Wen ◽  
Hui-Ying Hu ◽  
Long He ◽  
...  
Keyword(s):  
Banach Space ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Banach Spaces ◽  
Well Posedness ◽  
Mixed Variational Inequality ◽  
Mixed Variational Inequalities ◽  
Generalized Mixed Variational Inequality ◽  
Generalized Mixed Variational Inequalities

We introduce a new concept of Hadamard well-posedness of a generalized mixed variational inequality in a Banach space. The relations between the Levitin–Polyak well-posedness and Hadamard well-posedness for a generalized mixed variational inequality are studied. The characterizations of Hadamard well-posedness for a generalized mixed variational inequality are established.

scholarly journals Projection Methods for a System of Nonlinear Mixed Variational Inequalities in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Zhong-Bao Wang ◽  
Guo-Ji Tang ◽  
Hong-Ling Zhang
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Projection Operator ◽  
Existence And Uniqueness ◽  
Projection Methods ◽  
Uniqueness Of Solution ◽  
Mixed Variational Inequality ◽  
Mixed Variational Inequalities

The existence and uniqueness of solution for a system of nonlinear mixed variational inequality in Banach spaces is given firstly. A Mann iterative sequences with errors for this system of nonlinear mixed variational inequalities in Banach spaces is studied, by using the generalizedf-projection operatorπKf. Our results extend the main results in (Verma (2005); Verma (2001)) from Hilbert spaces to Banach spaces.

scholarly journals Well-Posedness by Perturbations of Generalized Mixed Variational Inequalities in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-38
Author(s):  
Lu-Chuan Ceng ◽  
Ching-Feng Wen
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Banach Spaces ◽  
Inclusion Problem ◽  
Point Problem ◽  
Well Posedness ◽  
Mixed Variational Inequality ◽  
Mixed Variational Inequalities ◽  
Generalized Mixed Variational Inequality ◽  
Generalized Mixed Variational Inequalities

We consider an extension of the notion of well-posedness by perturbations, introduced by Zolezzi (1995, 1996) for a minimization problem, to a class of generalized mixed variational inequalities in Banach spaces, which includes as a special case the class of mixed variational inequalities. We establish some metric characterizations of the well-posedness by perturbations. On the other hand, it is also proven that, under suitable conditions, the well-posedness by perturbations of a generalized mixed variational inequality is equivalent to the well-posedness by perturbations of the corresponding inclusion problem and corresponding fixed point problem. Furthermore, we derive some conditions under which the well-posedness by perturbations of a generalized mixed variational inequality is equivalent to the existence and uniqueness of its solution.

scholarly journals Connectedness of Solution Sets for Weak Vector Variational Inequalities on Unbounded Closed Convex Sets

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Ren-you Zhong ◽  
Yun-liang Wang ◽  
Jiang-hua Fan
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Convex Sets ◽  
Vector Variational Inequality ◽  
Vector Variational Inequalities ◽  
Solution Set ◽  
Solution Sets ◽  
Finite Dimensional ◽  
Path Connectedness ◽  
Weak Vector

We study the connectedness of solution set for set-valued weak vector variational inequality in unbounded closed convex subsets of finite dimensional spaces, when the mapping involved is scalarC-pseudomonotone. Moreover, the path connectedness of solution set for set-valued weak vector variational inequality is established, when the mapping involved is strictly scalarC-pseudomonotone. The results presented in this paper generalize some known results by Cheng (2001), Lee et al. (1998), and Lee and Bu (2005).

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 Vector and Ordered Variational Inequalities and Applications to Order-Optimization Problems on Banach Lattices

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Linsen Xie ◽  
Jinlu Li ◽  
Wenshan Yang
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Fixed Point Theorems ◽  
Optimization Problems ◽  
Banach Lattices ◽  
Variational Inequality Problems ◽  
Vector Spaces ◽  
Real Vector ◽  
Finite Dimensional

We investigate the connections between vector variational inequalities and ordered variational inequalities in finite dimensional real vector spaces. We also use some fixed point theorems to prove the solvability of ordered variational inequality problems and their application to some order-optimization problems on the Banach lattices.

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
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