- A Riemannian rank-adaptive method for low-rank optimization Guifang Zhou (zhouguifang2009gmail.com) Wen Huang (huwst08gmail.com) Kyle A. Gallivan (kgallivanfsu.edu) Paul Van Dooren (Paul.Vandoorenuclouvain.be) P.-A. Absil (absilinma.ucl.ac.be) Abstract: This paper presents an algorithm that solves optimization problems on a matrix manifold $\mathcal{M} \subseteq \mathbb{R}^{m \times n}$ with an additional rank inequality constraint. The algorithm resorts to well-known Riemannian optimization schemes on fixed-rank manifolds, combined with new mechanisms to increase or decrease the rank. The convergence of the algorithm is analyzed and a weighted low-rank approximation problem is used to illustrate the efficiency and effectiveness of the algorithm. Keywords: low-rank optimization; rank-constrained optimization; Riemannian manifold; fixed-rank manifold; low-rank approximation Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization ) Category 2: Applications -- Science and Engineering (Data-Mining ) Citation: Technical report UCL-INMA-2015.05 Download: [PDF]Entry Submitted: 01/27/2016Entry Accepted: 01/27/2016Entry Last Modified: 02/05/2016Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.