Rank-Constrainted Optimization: A Riemannian Ma nifold Approachy
2015
This paper presents an algorithm that solves optimization problems on a matrix manifold MR m×n with an additional rank inequality con- straint. New geometric objects are defined to facilitate efficiently finding a suitable rank. The convergence properties of the algorithm are given and a weighted low-rank approximation problem is used to illustrate the efficiency and effectiveness of the algorithm.
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