Global Stability Results for the Weak Vector Variational Inequality

2005 ◽  
Vol 32 (4) ◽  
pp. 543-550 ◽  
Author(s):  
Y. H. Cheng ◽  
D. L. Zhu
Keyword(s):  
Variational Inequality ◽  
Global Stability ◽  
Vector Variational Inequality ◽  
Stability Results ◽  
Weak Vector

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).

scholarly journals Continuity Results and Error Bounds on Pseudomonotone Vector Variational Inequalities via Scalarization

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Xin Zuo ◽  
Hong-Zhi Wei ◽  
Chun-Rong Chen
Keyword(s):  
Variational Inequality ◽  
Error Bounds ◽  
Vector Variational Inequality ◽  
Gap Functions ◽  
Strong Pseudomonotonicity ◽  
Solution Mapping ◽  
Constraint Set ◽  
Regularized Gap Functions ◽  
Lower And Upper Semicontinuities ◽  
Weak Vector

Continuity (both lower and upper semicontinuities) results of the Pareto/efficient solution mapping for a parametric vector variational inequality with a polyhedral constraint set are established via scalarization approaches, within the framework of strict pseudomonotonicity assumptions. As a direct application, the continuity of the solution mapping to a parametric weak Minty vector variational inequality is also discussed. Furthermore, error bounds for the weak vector variational inequality in terms of two known regularized gap functions are also obtained, under strong pseudomonotonicity assumptions.

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.

Stability of weak vector variational inequality

2009 ◽  
Vol 70 (4) ◽  
pp. 1528-1535 ◽  
Author(s):  
S.J. Li ◽  
C.R. Chen
Keyword(s):  
Variational Inequality ◽  
Vector Variational Inequality ◽  
Weak Vector
Sign in / Sign up

Export Citation Format

Share Document