  Due to the multi-linearity of tensors, most algorithms for tensor
optimization problems are designed based on the block coordinate descent
method. Such algorithms are widely employed by practitioners for their
implementability and effectiveness. However, these algorithms usually suffer
from the lack of theoretical guarantee of global convergence and analysis of
convergence rate. In this paper, we propose a block coordinate descent type
algorithm for the low rank partially orthogonal tensor approximation problem
and analyse its convergence behaviour. To achieve this, we carefully
investigate the variety of low rank partially orthogonal tensors and its
geometric properties related to the parameter space, which enable us to locate
KKT points of the concerned optimization problem. With the aid of these
geometric properties, we prove without any assumption that: (1) Our algorithm
converges globally to a KKT point; (2) For any given tensor, the algorithm
exhibits an overall sublinear convergence with an explicit rate which is
sharper than the usual $O(1/k)$ for first order methods in nonconvex
optimization; {(3)} For a generic tensor, our algorithm converges $R$-linearly.
