On the Finiteness Property of the Polynomial Complementarity Problem

This paper explores the finiteness of the solution set of the polynomial complementarity problem (PCP). To achieve this goal, we introduce two new classes of structured tensor tuples, namely the nondegenerate tensor tuple and the strong nondegenerate tensor tuple, as a generalization of nondegenerate tensors, and discuss their properties and interconnections. We investigate the finiteness of the solution set of the PCP in the context of these structured tensor tuples and establish a sufficient condition that guarantees a finite solution set. As a consequence, we establish a result related to the finiteness of the solution set of tensor complementarity problems.