Completely positive factorization by a Riemannian smoothing method
Zhijian Lai and
Akiko Yoshise ()
Additional contact information
Zhijian Lai: University of Tsukuba
Akiko Yoshise: University of Tsukuba
Computational Optimization and Applications, 2022, vol. 83, issue 3, No 7, 933-966
Abstract Copositive optimization is a special case of convex conic programming, and it consists of optimizing a linear function over the cone of all completely positive matrices under linear constraints. Copositive optimization provides powerful relaxations of NP-hard quadratic problems or combinatorial problems, but there are still many open problems regarding copositive or completely positive matrices. In this paper, we focus on one such problem; finding a completely positive (CP) factorization for a given completely positive matrix. We treat it as a nonsmooth Riemannian optimization problem, i.e., a minimization problem of a nonsmooth function over a Riemannian manifold. To solve this problem, we present a general smoothing framework for solving nonsmooth Riemannian optimization problems and show convergence to a stationary point of the original problem. An advantage is that we can implement it quickly with minimal effort by directly using the existing standard smooth Riemannian solvers, such as Manopt. Numerical experiments show the efficiency of our method especially for large-scale CP factorizations.
Keywords: Completely positive factorization; Smoothing method; Nonsmooth Riemannian optimization problem; 15A23; 15B48; 90C48; 90C59 (search for similar items in EconPapers)
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed
Downloads: (external link)
http://link.springer.com/10.1007/s10589-022-00417-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:83:y:2022:i:3:d:10.1007_s10589-022-00417-4
Ordering information: This journal article can be ordered from
Access Statistics for this article
Computational Optimization and Applications is currently edited by William W. Hager
More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().