A regularized Newton method for the efficient approximation of tensors represented in the canonical tensor format

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A literature survey of low‐rank tensor approximation techniques (2013, neutral): “More recent developments for general tensors include work on increasing the efficiency and robustness of gradient-based and Newton-like methods [2,73,75,141,224,225], modifying and improving ALS (alternating least squares) [42, 58, 59, 91, 226], studying the convergence of ALS [52, 195, 255] and red”
Low-rank tensor methods for linear systems and eigenvalue problems (2012, background): “Unfortunately, developing a robust and efficient algorithm, which yields an approximation to any desirable accuracy for this format, remains a subtle problem, see [1, 20] for recent progress.”
Variational calculus with sums of elementary tensors of fixed rank (2012, unknown): “Problem (i) above] has recently been proven [9,31].”
Low-Rank Tensor Krylov Subspace Methods for Parametrized Linear Systems (2011, methodology): “Recently developed methods for low-rank approximation in CP decomposition can be found in [1, 14, 30] and overcome some of these subtleties.”
Efficient Analysis of High Dimensional Data in Tensor Formats (2012, methodology): “Let v ∈ RR, ε > 0 and Ucp(x̂) a solution of the approximation problem as analysed in [10, 13, 12].”
Algorithm 941 (2014, background): “Unfortunately, developing a robust and efficient algorithm for this format, which yields an approximation to any desirable accuracy, remains a subtle problem, see [1, 7] for recent progress.”