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A New Gap Function for Vector Variational Inequalities with an Application
Joint Authors
O'Regan, Donal
Wu, Meng
Huang, Nan-Jing
Ma, Hui-qiang
Source
Journal of Applied Mathematics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-06-19
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
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،Vol. 2013, no. 2013, pp.1-8.
https://search.emarefa.net/detail/BIM-470978
Modern Language Association (MLA)
Ma, Hui-qiang…[et al.]. A New Gap Function for Vector Variational Inequalities with an Application. Journal of Applied Mathematics No. 2013 (2013), pp.1-8.
https://search.emarefa.net/detail/BIM-470978
American Medical Association (AMA)
Ma, Hui-qiang& Huang, Nan-Jing& Wu, Meng& O'Regan, Donal. A New Gap Function for Vector Variational Inequalities with an Application. Journal of Applied Mathematics. 2013. Vol. 2013, no. 2013, pp.1-8.
https://search.emarefa.net/detail/BIM-470978
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-470978