Finding the extreme Z-eigenvalues of tensors via a sequential semidefinite programming method

In this paper, we first introduce the tensor conic linear programming (TCLP), which is a generalization of the space TCLP. Then an approximation method, by using a sequence of semidefinite programming problems, is proposed to solve the TCLP. In particular, we reformulate the extreme Z-eigenvalue problem as a special TCLP. It gives a numerical algorithm to compute the extreme Z-eigenvalue of an even order tensor with dimension larger than three, which improves the literature. Numerical experiments show the efficiency of the proposed method.