Global error bounds for the tensor complementarity problem with a P-tensor

Mengmeng Zheng; Ying Zhang; Zheng-Hai Huang

doi:10.3934/jimo.2018078

Article Contents

2019, Volume 15, Issue 2: 933-946. Doi: 10.3934/jimo.2018078

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Global error bounds for the tensor complementarity problem with a P-tensor

School of Mathematics, Tianjin University, Tianjin 300350, China

* Corresponding author: Zheng-Hai Huang
* Corresponding author: Zheng-Hai Huang

Received: August 31, 2017

Revised: December 31, 2017

Early access: June 2018

Published: January 2019

The third author is supported by the National Natural Science Foundation of China (Grant No. 11431002).

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As a natural extension of the linear complementarity problem, the tensor complementarity problem has been studied recently; and many theoretical results have been obtained. In this paper, we investigate the global error bound for the tensor complementarity problem with a P-tensor. We give two global error bounds for this class of complementarity problems with the help of two positively homogeneous operators defined by a P-tensor. When the order of the involved tensor reduces to 2, the results obtained in this paper coincide exactly with the one for the linear complementarity problem.

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Mathematics Subject Classification: Primary: 90C33, 65K10; Secondary: 15A69.

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