Rank-constrained optimization: A Riemannian manifold approach
Guifang Zhou, Wen Tao Huang, Kyle A. Gallivan, Paul Van Dooren, Pierre-Antoine Absil · Digital Access to Libraries (Université catholique de Louvain (UCL), l'Université de Namur (UNamur) and the Université Saint-Louis (USL-B)) · 2015
This paper presents an algorithm that solves optimization problems on a matrix manifold M ⊆ R with an additional rank inequality constraint. 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.