On the best low multilinear rank approximation of higher-order tensors

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Quasi-Newton Methods on Grassmannians and Multilinear Approximations of Tensors (2009, methodology): “Like the Newton–Grassmann (NG) algorithms in [24, 33] and the trust-region approach in [32, 31], the quasi-Newton algorithms proposed in this article have guaranteed convergence to stationary points and represent an improvement over Gauss– Seidel-type coordinate-cycling heuristics like alternating l”
Krylov-Type Methods for Tensor Computations (2010, unknown): “An important thread of research in this field is the computation of low multilinear rank approximations of tensors [21,6,7,1,33,5,9,28,15,25,17,20].”
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].”
Jacobi Algorithm for the Best Low Multilinear Rank Approximation of Symmetric Tensors (2013, methodology): “Recent iterative algorithms solving the problem include geometric Newton [21, 29], quasi-Newton [45], trust-region [27], and particle swarm optimization [4] algorithms.”
A New Truncation Strategy for the Higher-Order Singular Value Decomposition (2012, methodology): “For instance, the T-HOSVD is used to initialize iterative algorithms to compute the best rank-1 approximation [7, 28, 63] or best approximation of a specified multilinear rank [11, 15, 24, 26, 51].”