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High-order Copositive Tensors and its Applications
Keywords:Copositive tensor; Tensor complementarity problem; Homogeneous polynomial; Tensor eigenvalue; Hypergraphs
      With the coming of the big data era, high-order high-dimensional structured tensors received much attentions of researchers'' in recent years, and now they are developed into a new research branch in mathematics named multilinear algebra. As a special kind of structured tensor, the copositive tensor receives a special concern due to its wide applications in vacuum stability of a general scalar potential, polynomial optimization, tensor complementarity problem and tensor eigenvalue complementarity problem. In this review, we will give a simple survey on recent advances of high-order copositive tensors and its applications. Some potential research directions in the future are also listed in the paper.