Judgment And Algorithm Of Rectangular Tensor Copositivity

As a tool,tensor is widely used in high-order statistical analysis,multidimensional data analysis and even-order homogeneous polynomial determination.As a special tensor,the copositive tensor has many excellent properties and has important applications in tensor complementarity and polynomial optimization problems.Based on this,the properties of the copositive tensor are studied,and on this basis,Some criterias for determinsing the copositive tensor are established.For the symmetric copositive tensor,iterative algorithms for determining the copositivity of the symmetric tensor is established based on the theory of polynomial optimization,standard simplex and its partition,respectively.In this paper,we mainly study the necessary,sufficient,sufficient and necessary conditions for the partially symmetric rectangular copositive tensor and the criteria for determining the copositivity of the tensor.Based on the theory of standard simplex and its partition,this paper explores the necessary,sufficient and necessary conditions for a rectangular tensor to be a copositive tensor,and designs an algorithm to determine the copositive tensor according to the conclusions obtained.The effectiveness of the algorithm is verified by numerical examples.