Partially symmetric nonnegative rectangular tensors and copositive rectangular tensors

Yining Gu; Wei Wu

doi:10.3934/jimo.2018070

Article Contents

2019, Volume 15, Issue 2: 775-789. Doi: 10.3934/jimo.2018070

This issue Previous Article A proximal-projection partial bundle method for convex constrained minimax problems Next Article Henig proper efficiency in vector optimization with variable ordering structure

Partially symmetric nonnegative rectangular tensors and copositive rectangular tensors

Yining Gu and
Wei Wu^,

School of Mathematical Sciences, Tianjin University, Tianjin 300350, China

* Corresponding author: Wei Wu
* Corresponding author: Wei Wu

Received: August 31, 2016

Revised: November 30, 2017

Early access: June 2018

Published: January 2019

This work was supported by NSF grant of China (Grant No. 11371276).

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Abstract

In this paper, we prove a maximum property of the largest H-singular value of a partially symmetric nonnegative rectangular tensor, and establish some bounds for this singular value. Then we give the definition of copositive rectangular tensors. This concept extends from the concept of copositive square tensors. Partially symmetric nonnegative rectangular tensors and positive semi-definite rectangular tensors are examples of copositive rectangular tensors. We establish some necessary conditions and some sufficient conditions for a real partially symmetric rectangular tensor to be a copositive rectangular tensor. We also give an equivalent definition of strictly copositive rectangular tensors. Moreover, some further properties of copositive rectangular tensors are discussed.

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Mathematics Subject Classification: Primary: 15A18, 15A69, 15A72.

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