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January  2008, 4(1): 155-165. doi: 10.3934/jimo.2008.4.155

On the stability of a dual weak vector variational inequality problem

S. J. Li 1, and  Z. M. Fang 1,

1. 

College of Mathematics and Science, Chongqing University, Chongqing, 400044, China, China

Received  November 2006 Revised  June 2007 Published  January 2008

In this paper, we obtain some stability results for the dual problem of a weak vector variational inequality problem. We establish the upper semicontinuity property of the solution set for a perturbed dual problem of a weak vector variational inequality problem. By virtue of a parametric gap function and a key assumption, we also obtain the lower semicontinuity property of the solution set for the perturbed dual problem. Some examples are given for the illustration of the necessity of our research on duality.
Keywords: parametric gap function., upper semicontinuity, Dual weak vector variational inequality, nonlinear scalarization function, lower semicontinuity.
Mathematics Subject Classification: 90C31, 49J5.
Citation: S. J. Li, Z. M. Fang. On the stability of a dual weak vector variational inequality problem. Journal of Industrial & Management Optimization, 2008, 4 (1) : 155-165. doi: 10.3934/jimo.2008.4.155
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