American Institute of Mathematical Sciences

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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

C. R. Chen 1, and  S. J. Li 1,

1. 

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

Received  September 2006 Revised  December 2006 Published  July 2007

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 and Management Optimization, 2007, 3 (3) : 519-528. doi: 10.3934/jimo.2007.3.519
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