Solution maps of polynomial variational inequalities

In this paper, we investigate several properties of the solution maps of variational inequalities with polynomial data. First, we prove some facts on the $R_0$-property, the local boundedness, and the upper semicontinuity of the solution maps. Second, we establish results on the solution existence and the local upper-H\"{o}lder stability under the copositivity condition. Third, when the constraint set is semi-algebraic, we discuss the genericity of the $R_0$-property and the finite-valuedness of the solution maps.