A self-adaptive trust region method for extreme B-eigenvalues of symmetric tensors

A self-adaptive trust region method is presented for finding the largest or smallest B-eigenvalues of symmetric tensors. One of the important features of this method is that B-eigenvalues problem of symmetric tensors is transformed into a homogenous polynomial optimization. Global convergence of the proposed algorithm and second-order necessary conditions of the optimal solutions are established, respectively. Numerical experiments are listed to illustrate the efficiency of the proposed method.