Abstract
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.
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Chen, Y. Successive unconstrained dual optimization method for rank-one approximation to tensors. J. Appl. Math. Comput. 38, 9–23 (2012). https://doi.org/10.1007/s12190-010-0459-7
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DOI: https://doi.org/10.1007/s12190-010-0459-7