Quasi-Newton Methods on Grassmannians and Multilinear Approximations of Tensors

@article{Savas2010QuasiNewtonMO,
  title={Quasi-Newton Methods on Grassmannians and Multilinear Approximations of Tensors},
  author={Berkant Savas and Lek-Heng Lim},
  journal={SIAM J. Scientific Computing},
  year={2010},
  volume={32},
  pages={3352-3393}
}
In this paper we proposed quasi-Newton and limited memory quasi-Newton methods for objective functions defined on Grassmannians or a product of Grassmannians. Specifically we defined bfgs and l-bfgs updates in local and global coordinates on Grassmannians or a product of these. We proved that, when local coordinates are used, our bfgs updates on Grassmannians share the same optimality property as the usual bfgs updates on Euclidean spaces. When applied to the best multilinear rank approximation… CONTINUE READING