Monotone affine vector variational inequalities

Abstract

By using a stability theorem of S.M. Robinson and a scalarization method, we establish sufficient conditions for the upper semicontinuity of the solution maps of parametric monotone affine vector variational inequalities. As a by-product, some new topological properties of the solution sets of these problems are obtained. Our results imply several facts for the solution stability and connectedness of the solution sets of convex quadratic vector optimization problems and of linear fractional vector optimization problems.

Keywords:

• affine variational inequality
• affine vector variational inequality
• solution set
• scalarization
• upper-Lipschitz continuity
• upper semicontinuity
• connectedness

AMS Subject Classifications::

• 90C31
• 90C29
• 49J40
• 49J53
• 49K40

Acknowledgements

This work was supported by National Sun Yat-Sen University (Kaohsiung, Taiwan) and National Foundation for Science & Technology Development (Vietnam). The authors would like to thank Mr Nguyen Huy Chieu for his useful remarks on the first version of this article. We are indebted to the referees for their very careful reading, insightful comments, and valuable suggestions.