关于CopositivePlus张量及其互补问题的研究

On CopositivePlus Tensor and Tensor Complementarity Problem

近年来,关于张量(超矩阵)的研究得到了越来越多的关注.相应的互补问题张量互补问题(TCP),也得到了广泛研究.本文延伸CopositivePlus矩阵的概念到高阶张量的情形,定义了一类新的结构张量,称为Copositive-Plus张量,并对其性质进行了研究;并且证明,当所涉及的张量是Q张量和CopositivePlus时,对应的张量互补问题的解集是有界的.

In recent years,researches on tensor(hypermatrices)have received more and more attention.The tensor complementarity problem(TCP),correspondingly,has also been extensively studied.In this paper,we extend the concept of CopositivePlus matrix to the case of tensor.We define a class of structured tensors,called CopositivePlus tensor,and study its properties.We prove that the solution set of a tensor complementarity problem is nonempty and bounded when the involved tensor is a Q tensor and a CopositivePlus tensor.