Successive unconstrained dual optimization method for rank-one approximation to tensors

A successive unconstrained dual optimization (SUDO) method is developed to solve the high order tensors’ best rank-one approximation problems, in the least-squares sense. The constrained dual program of tensors’ rank-one approximation is transformed into a sequence of unconstrained optimization problems, for where a fast gradient method is proposed. We introduce the steepest ascent direction, a initial step length strategy and a backtracking line search rule for each iteration. A proof of the global convergence of the SUDO algorithm is given. Preliminary numerical experiments show that our method outperforms the alternating least squares (ALS) method.