Riemannian optimization on tensor products of Grassmann manifolds: applications to generalized Rayleigh-quotients (Q2903120)

The authors consider a class of constrained Riemannian optimization problem by introducing a generalized Rayleigh quotient on the direct product of Grasmannian manifolds. These kind of optimization problems arise in various application areas such as low-rank tensor approximations in statistics, signal processing, and data compression; geometric measures of pure state entanglement from quantum computing; subspace reconstruction problems from image processing; sorting tasks from combinatorics.NEWLINENEWLINEThey give characterization of the critical points of the Rayleigh quotient and non-degeneracy conditions for the Hessians. They introduce Newton-like and conjugate gradient methods for optimization of high dimensional tensors. Based on numerical experiments, the conjugate gradient method turns to be a better candidate for this kind of large scale problems with low computation cost and fast computational time.