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-Hölder 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.

中文翻译：

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多项式变分不等式的解图

在本文中，我们研究了具有多项式数据的变分不等式解图的几个性质。首先，我们证明\（R_0 \） -属性，局部有界和解映射的上半连续性。其次，我们建立了在共性条件下解存在性和局部上Hölder稳定性的结果。第三，当约束集为半代数时，我们讨论\（R_0 \） -属性的泛型和解映射的有限值。