Projection algorithms for nonconvex minimization with application to sparse principal component analysis

William W. Hager (), Dzung T. Phan () and Jiajie Zhu ()
Additional contact information
William W. Hager: University of Florida
Dzung T. Phan: IBM T. J. Watson Research Center
Jiajie Zhu: University of Florida

Journal of Global Optimization, 2016, vol. 65, issue 4, No 2, 657-676

Abstract: Abstract We consider concave minimization problems over nonconvex sets. Optimization problems with this structure arise in sparse principal component analysis. We analyze both a gradient projection algorithm and an approximate Newton algorithm where the Hessian approximation is a multiple of the identity. Convergence results are established. In numerical experiments arising in sparse principal component analysis, it is seen that the performance of the gradient projection algorithm is very similar to that of the truncated power method and the generalized power method. In some cases, the approximate Newton algorithm with a Barzilai–Borwein Hessian approximation and a nonmonotone line search can be substantially faster than the other algorithms, and can converge to a better solution.

Keywords: Sparse principal component analysis; Gradient projection; Nonconvex minimization; Approximate Newton; Barzilai–Borwein method (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10898-016-0402-z 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:jglopt:v:65:y:2016:i:4:d:10.1007_s10898-016-0402-z

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/10898

DOI: 10.1007/s10898-016-0402-z

Access Statistics for this article

Journal of Global Optimization is currently edited by Sergiy Butenko

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