Semicontinuity of the solution set map to a set-valued weak vector variational inequality

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July 2007, 3(3): 519-528. doi: 10.3934/jimo.2007.3.519

Semicontinuity of the solution set map to a set-valued weak vector variational inequality

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

Received September 2006 Revised December 2006 Published July 2007

Abstract
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This paper investigates the semicontinuity of the solution set map for a parametric set-valued weak vector variational inequality in Banach spaces. The upper semicontinuity and closedness of the solution set map are obtained. A parametric gap function is proposed by using a nonlinear scalarization function. By virtue of the parametric gap function and a key assumption, the lower semicontinuity of the solution set map is established.

Keywords: parametric gap function, nonlinear scalarization function, upper semicontinuity, set-valued weak vector variational inequality., Lower semicontinuity.

Mathematics Subject Classification: 90C31, 49J5.

Citation: C. R. Chen, S. J. Li. Semicontinuity of the solution set map to a set-valued weak vector variational inequality. Journal of Industrial & Management Optimization, 2007, 3 (3) : 519-528. doi: 10.3934/jimo.2007.3.519

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