Differential-geometric Newton method for the best rank-(R1, R2, R3) approximation of tensors

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A literature survey of low‐rank tensor approximation techniques (2013, neutral): “Examples include nonlinear conjugate gradient or Newton-like methods on manifolds of low-rank matrices [35, 191, 198, 257, 258] or low-rank tensors [52, 53, 131, 132, 255], see also Section 3.”
Wedderburn Rank Reduction and Krylov Subspace Method for Tensor Approximation. Part 1: Tucker Case (2010, methodology): “For a tensor given as a full array of elements, the multilinear SVD provides a quasi-optimal Tucker approximation which further can be refined by different iterative methods such that Tucker-ALS [22, 7], Newton-Grassmann [10, 19], etc.”
Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 2 Applications and Future Perspectives (2017, methodology): “…(also called the differential geometric optimization) has been successfully applied to the computation of the best Tucker approximation [Ishteva et al., 2009, 2011, Steinlechner, 2016a], whereby the Tucker manifold structure can be formulated through a set of Tucker tensors of fixed…”
Riemannian Optimization on Tensor Products of Grassmann Manifolds: Applications to Generalized Rayleigh-Quotients (2010, methodology): “Newton algorithms have been proposed in [8, 18], quasi-Newton methods in [28], conjugated gradient and trust region methods in [17].”