On the Finiteness Property of the Polynomial Complementarity Problem

TL;DR

This paper investigates conditions under which the solution set of the polynomial complementarity problem is finite, introducing new tensor classes and establishing sufficient conditions for finiteness.

Contribution

It introduces nondegenerate and strong nondegenerate tensor classes and links their properties to the finiteness of PCP solutions, advancing theoretical understanding.

Findings

Established sufficient conditions for finite solution sets

Introduced new structured tensor classes

Connected tensor properties to solution finiteness

Abstract

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.