Copositive tensor optimization problem and its applications to hypergraphs

. In this paper, we consider the copositive optimization problem with high-order copositive tensors, which can be used to estimate the coclique number of uniform hypergraphs. Firstly, we present a checkable equivalent condition for the Slater constraint qualification. Then, based on the standard simplex, we focus on solving a new kind of CTOP from hypergraph theory. To do that, two approximation problems are established and a linear approximation algorithm is proposed for the original CTOP. It is proven that the optimal value of the original problem lies between the optimal values of the two approximation problems. Furthermore, relationships between the optimal solutions are considered. Finally, the proposed algorithm is applied to estimate the coclique number of uniform hypergraphs, and numerical results show its efficiency.