Publication

A new gap function for vector variational inequalities with an application

Ma, Hui-qiang
; 
Huang, Nan-jing
; 
Wu, Meng
; 
O'Regan, Donal
Identifiers
http://hdl.handle.net/10379/12540
 https://doi.org/10.13025/26580
Publication Date
2013-01-01
Keywords
linear complementarity-problems, residual minimization method, sensitivity properties, traffic equilibrium, stability, existence
Type
Article
Downloads
Show all metadata
Citation
Ma, Hui-qiang; Huang, Nan-jing; Wu, Meng; O'Regan, Donal (2013). A new gap function for vector variational inequalities with an application. Journal of Applied Mathematics ,
Abstract
We consider a vector variational inequality in a finite-dimensional space. A new gap function is proposed, and an equivalent optimization problem for the vector variational inequality is also provided. Under some suitable conditions, we prove that the gap function is directionally differentiable and that any point satisfying the first-order necessary optimality condition for the equivalent optimization problem solves the vector variational inequality. As an application, we use the new gap function to reformulate a stochastic vector variational inequality as a deterministic optimization problem. We solve this optimization problem by employing the sample average approximation method. The convergence of optimal solutions of the approximation problems is also investigated.
Funder
Publisher
Hindawi Limited
Publisher DOI
Rights
Attribution-NonCommercial-NoDerivs 3.0 Ireland
cbn
Collections
Externally hosted open access publications with University of Galway authors (2)