A Riemannian Trust Region Method for the Canonical Tensor Rank Approximation Problem

@article{Breiding2018ART,
  title={A Riemannian Trust Region Method for the Canonical Tensor Rank Approximation Problem},
  author={Paul Breiding and Nick Vannieuwenhoven},
  journal={SIAM J. Optim.},
  year={2018},
  volume={28},
  pages={2435-2465}
}
The canonical tensor rank approximation problem (TAP) consists of approximating a real-valued tensor by one of low canonical rank, which is a challenging non-linear, non-convex, constrained optimization problem, where the constraint set forms a non-smooth semi-algebraic set. We introduce a Riemannian Gauss-Newton method with trust region for solving small-scale, dense TAPs. The novelty of our approach is threefold. First, we parametrize the constraint set as the Cartesian product of Segre… 
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