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Journal of Function Spaces
Volume 2016, Article ID 7297854, 11 pages
http://dx.doi.org/10.1155/2016/7297854
Research Article

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

College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China

Received 31 August 2015; Accepted 11 January 2016

Academic Editor: Giuseppe Marino

Copyright © 2016 Xin Zuo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.