有限维空间中逆变分不等式的性质及应用
The Properties and Applications of the Inverse Variational Inequalities in Finite-Dimensional Space

逆变分不等式在经济、管理和交通网络等领域都有着重要的应用。本文运用压缩映像原理证明了Lipschitz连续和强单调条件下有限维空间中逆变分不等式解的存在唯一性，并且以春节前后为疏散人流对不同的日子确定不同的合理票价问题为例，给出了逆变分不等式在交通领域的应用。
The inverse variational inequality has important applications in fields such as economics, management, and transportation networks. In this paper, the existence and uniqueness of the solution to the inverse variational inequality in a finite-dimensional space under the conditions of Lipschitz continuity and strong monotonicity are proved using the compression mapping principle. An example is given to illustrate the application of the inverse variational inequality in the field of transportation, where the reasonable ticket prices for dispersing passenger flow during the Spring Festival period are determined for different days based on the inverse variational inequality.