Abstract
The goal of this paper is to investigate a class of vertical polynomial complementarity problems (denoted by VPCP), which is a subclass of complementarity problems. Firstly, we give a necessary and sufficient condition for the existence of solution for the VPCP. Secondly, the existence of the least element solution to the VPCP is shown when the involved tensor tuple is a vertical block Z-tensor tuple and the feasible set of the problem is nonempty. Particularly, we can find the least element solution of this problem by solving a polynomial optimization problem. In addition, some examples are given to demonstrate the validity of our findings.
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