Convergence conjecture for the coordinate-descent PARAFAC algorithm

Let $\{\mathbf{A}^k\}$ be the sequence generated by Algorithm, where $\mathbf{A}^k$ is the solution $(\mathbf{A}^{(1)},\mathbf{A}^{(2)},\ldots,\mathbf{A}^{(N)})$ in the $k$-th iteration of the repeat loop. Assume that $\{\mathbf{A}^k\}$ is bounded. Convergence conjecture. The sequence $\{\mathbf{A}^k\}$ converges to a critical point $\bar{\mathbf{A}}$. The convergence theorem for this multiconvex stochastic scheme is not clear; the conjecture asserts convergence under boundedness, while no proof or resolution is supplied here.