On some properties of $\omega$-uniqueness in tensor complementarity problem

TL;DR

This paper introduces column adequate tensors in tensor complementarity problems, explores their properties, and shows conditions under which these problems have a unique solution, advancing understanding of solution uniqueness in nonlinear tensor problems.

Contribution

The paper defines column adequate tensors and proves their inheritance and invariance properties, establishing conditions for $\, ext{TCP}(q, ext{A})$ to have a unique solution.

Findings

Column adequate tensors are introduced and characterized.

Inheritance and invariance properties of these tensors are established.

Conditions for $\, ext{TCP}(q, ext{A})$ to have a unique solution are identified.

Abstract

In this article we introduce column adequate tensor in the context of tensor complementarity problem and consider some important properties. The tensor complementarity problem is a class of nonlinear complematarity problems with the involved function being defined by a tensor. We establish the inheritance property and invariant property of column adequate tensors. We show that TCP$(q,\mathcal{A})$ has $\omega$-unique solution under some assumptions.