A dual spectral projected gradient method for log-determinant semidefinite problems

Takashi Nakagaki, Mituhiro Fukuda (), Sunyoung Kim () and Makoto Yamashita ()
Additional contact information
Takashi Nakagaki: Tokyo Institute of Technology
Mituhiro Fukuda: Tokyo Institute of Technology
Sunyoung Kim: Ewha W. University
Makoto Yamashita: Tokyo Institute of Technology

Computational Optimization and Applications, 2020, vol. 76, issue 1, No 2, 33-68

Abstract: Abstract We extend the result on the spectral projected gradient method by Birgin et al. in 2000 to a log-determinant semidefinite problem with linear constraints and propose a spectral projected gradient method for the dual problem. Our method is based on alternate projections on the intersection of two convex sets, which first projects onto the box constraints and then onto a set defined by a linear matrix inequality. By exploiting structures of the two projections, we show that the same convergence properties can be obtained for the proposed method as Birgin’s method where the exact orthogonal projection onto the intersection of two convex sets is performed. Using the convergence properties, we prove that the proposed algorithm attains the optimal value or terminates in a finite number of iterations. The efficiency of the proposed method is illustrated with the numerical results on randomly generated synthetic/deterministic data and gene expression data, in comparison with other methods including the inexact primal–dual path-following interior-point method, the Newton-CG primal proximal-point algorithm, the adaptive spectral projected gradient method, and the adaptive Nesterov’s smooth method. For the gene expression data, our results are compared with the quadratic approximation for sparse inverse covariance estimation method. We show that our method outperforms the other methods in obtaining a better objective value fast.

Keywords: Dual spectral projected gradient methods; Log-determinant semidefinite programs with linear constraints; Dual problem; Theoretical convergence results; Computational efficiency; 90C20; 90C22; 90C25; 90C26 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10589-020-00166-2 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:coopap:v:76:y:2020:i:1:d:10.1007_s10589-020-00166-2

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-020-00166-2

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 ().