  In this paper, we propose a new unified optimization algorithm for general
tensor decomposition which is formulated as an inverse problem for low-rank
tensors in the general linear observation models. The proposed algorithm
supports three basic loss functions ($\ell_2$-loss, $\ell_1$-loss and KL
divergence) and various low-rank tensor decomposition models (CP, Tucker, TT,
and TR decompositions). We derive the optimization algorithm based on
hierarchical combination of the alternating direction method of multiplier
(ADMM) and majorization-minimization (MM). We show that wide-range applications
can be solved by the proposed algorithm, and can be easily extended to any
established tensor decomposition models in a {plug-and-play} manner.
