scholarly journals Existence Results for New Weak and Strong Mixed Vector Equilibrium Problems on Noncompact Domain

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Ali Farajzadeh ◽  
Kasamsuk Ungchittrakool ◽  
Apisit Jarernsuk
Keyword(s):  
Variational Inequality ◽  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Existence Results ◽  
Vector Variational Inequality ◽  
Vector Equilibrium Problem ◽  
Variational Inequality Problems ◽  
Vector Equilibrium Problems ◽  
Noncompact Domain ◽  
Vector Equilibrium

We introduce and consider two new mixed vector equilibrium problems, that is, a new weak mixed vector equilibrium problem and a new strong mixed vector equilibrium problem which are combinations of certain vector equilibrium problems, and vector variational inequality problems. We prove existence results for the problems in noncompact setting.

scholarly journals Nonlinear Vector Variational Inequality Problems for η-Pseudomonotone Maps

2007 ◽  
Vol 2007 ◽  
pp. 1-6
Author(s):  
A. P. Farajzadeh
Keyword(s):  
Variational Inequality ◽  
Existence Result ◽  
Complementarity Problems ◽  
Vector Variational Inequality ◽  
Variational Inequality Problems ◽  
Vector Spaces ◽  
Topological Vector Spaces ◽  
New Class ◽  
Pseudomonotone Maps ◽  
Nonlinear Vector

We consider a new class of complementarity problems for η-pseudomonotone maps and obtain an existence result for their solutions in real Hausdorff topological vector spaces. Our results extend the same previous results in this literature.

scholarly journals Convergence Analysis of the Approximation Problems for Solving Stochastic Vector Variational Inequality Problems

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8 ◽  
Author(s):  
Meiju Luo ◽  
Kun Zhang
Keyword(s):  
Variational Inequality ◽  
Objective Function ◽  
Vector Variational Inequality ◽  
Low Risk ◽  
Variational Inequality Problems ◽  
Stationary Points ◽  
Conditional Value At Risk ◽  
Convergence Results ◽  
Approximation Problems ◽  
Stochastic Vector

In this paper, we consider stochastic vector variational inequality problems (SVVIPs). Because of the existence of stochastic variable, the SVVIP may have no solutions generally. For solving this problem, we employ the regularized gap function of SVVIP to the loss function and then give a low-risk conditional value-at-risk (CVaR) model. However, this low-risk CVaR model is difficult to solve by the general constraint optimization algorithm. This is because the objective function is nonsmoothing function, and the objective function contains expectation, which is not easy to be computed. By using the sample average approximation technique and smoothing function, we present the corresponding approximation problems of the low-risk CVaR model to deal with these two difficulties related to the low-risk CVaR model. In addition, for the given approximation problems, we prove the convergence results of global optimal solutions and the convergence results of stationary points, respectively. Finally, a numerical experiment is given.

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