Interval B-Tensors and Interval Double B-Tensors

TL;DR

This paper extends the theory of interval tensors by characterizing interval B-tensors and double B-tensors, providing verifiable conditions and exploring their connections to other tensor classes, with applications in optimization and uncertainty analysis.

Contribution

It introduces necessary and sufficient conditions for interval B-tensors and double B-tensors, linking them to other structured tensors and extending interval matrix theory to tensors.

Findings

Interval B-tensors and double B-tensors are characterized by extreme point tensors.

Connections between interval B-tensors and other structured tensors are established.

Under certain conditions, these tensors are shown to be interval P-tensors.

Abstract

This paper systematically investigates the properties and characterization of interval B-tensors and interval double B-tensors. We propose verifiable necessary and sufficient conditions that allow for determining whether an entire interval tensor family belongs to these classes based solely on its extreme point tensors. The study elucidates profound connections between these interval tensors and other structured ones such as interval Z-tensors and P-tensors, while also providing simplified criteria for special cases like circulant structures. Furthermore, under the condition of even order and symmetry, we prove that interval B-tensors (double B-tensors) ensure the property of being an interval P-tensor. This work extends interval matrix theory to tensors, offering new analytical tools for fields such as polynomial optimization and complementarity problems involving uncertainty.