In this paper, we mainly focus on the existence and uniqueness of the vertical tensor complementarity problem. Firstly, combining the generalized-order linear complementarity problem with the tensor complementarity problem, the vertical tensor complementarity problem is introduced. Secondly, we define some sets of special tensors, and illustrate the inclusion relationships. Finally, we show that the solution set of the vertical tensor complementarity problem is bounded under certain conditions, and some sufficient conditions for the existence and uniqueness of the solution of the vertical tensor complementarity problem are obtained from the view of the degree theory and the equal form of the minimum function.

翻译：在本文中,我们主要侧重于纵向高压互补问题的存在和独特性;首先,将普遍顺序线性互补问题与极端互补问题结合起来,提出了纵向高压互补问题;其次,我们界定了几组特殊点,并举例说明了包容性关系;最后,我们表明,纵向高压互补问题的解决办法在某些条件下是受约束的,从程度理论和最低功能的平等形式来看,为纵向高压互补问题的解决办法的存在和独特性提供了一些充分的条件。