Quartic First-Order Methods for Low-Rank Minimization

Radu-Alexandru Dragomir (), Alexandre d’Aspremont () and Jérôme Bolte
Additional contact information
Radu-Alexandru Dragomir: Université Toulouse 1 Capitole & D.I. École Normale Supérieure
Alexandre d’Aspremont: CNRS & D.I. École Normale Supérieure

Journal of Optimization Theory and Applications, 2021, vol. 189, issue 2, No 1, 363 pages

Abstract: Abstract We study a general nonconvex formulation for low-rank minimization problems. We use recent results on non-Euclidean first-order methods to provide efficient and scalable algorithms. Our approach uses the geometry induced by the Bregman divergence of well-chosen kernel functions; for unconstrained problems, we introduce a novel family of Gram quartic kernels that improve numerical performance. Numerical experiments on Euclidean distance matrix completion and symmetric nonnegative matrix factorization show that our algorithms scale well and reach state-of-the-art performance when compared to specialized methods.

Keywords: Bregman first-order methods; Low-rank minimization; Burer–Monteiro; Matrix factorization; Euclidean distance matrix completion; 90C06; 90C26 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-021-01820-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:189:y:2021:i:2:d:10.1007_s10957-021-01820-3

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-021-01820-3

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().