On the stability of a dual weak vector variational inequality problem

S. J. Li; Z. M. Fang

doi:10.3934/jimo.2008.4.155

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2008, Volume 4, Issue 1: 155-165. Doi: 10.3934/jimo.2008.4.155

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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

Received: October 31, 2006

Revised: May 31, 2007

Published: December 2007

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Abstract

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:

Dual weak vector variational inequality,
upper semicontinuity,
lower semicontinuity,
nonlinear scalarization function,
parametric gap function.

Mathematics Subject Classification: 90C31, 49J53.

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