Rank-constrained Optimization: A Riemannian Manifold approach

Authors

Guifang Zhou, Wen Huang, Kyle A. Gallivan, Paul Van Dooren, P.-A. Absil

Abstract

This paper presents an algorithm that solves optimization problems on a matrix manifold $\mathcal{M} \subset \mathbb{R}^{m \times n}$ 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.

Status

In Proceeding of European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN 2015)

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BibTex entry

Technical Report
@TECHREPORT{ZHGVA2015,
author = "Guifang Zhou and Wen Huang and Kyle A. Gallivan and Paul {Van Dooren} and P.-A. Absil",
title = "Rank-constrained Optimization: A Riemannian Manifold approach",
institution = "U.C.Louvain",
year = 2015,
number = "UCL-INMA-2015.02",
month = "January",
}