The Bound-Constrained Conjugate Gradient Method for Non-negative Matrices

Edwin A. H. Vollebregt ()
Additional contact information
Edwin A. H. Vollebregt: Delft University of Technology

Journal of Optimization Theory and Applications, 2014, vol. 162, issue 3, No 14, 953 pages

Abstract: Abstract Existing conjugate gradient (CG)-based methods for convex quadratic programs with bound constraints require many iterations for solving elastic contact problems. These algorithms are too cautious in expanding the active set and are hampered by frequent restarting of the CG iteration. We propose a new algorithm called the Bound-Constrained Conjugate Gradient method (BCCG). It combines the CG method with an active-set strategy, which truncates variables crossing their bounds and continues (using the Polak–Ribière formula) instead of restarting CG. We provide a case with n=3 that demonstrates that this method may fail on general cases, but we conjecture that it always works if the system matrix A is non-negative. Numerical results demonstrate the effectiveness of the method for large-scale elastic contact problems.

Keywords: Quadratic program; Bound constraints; Conjugate gradients method; Active set algorithm; Elastic contact problem (search for similar items in EconPapers)
Date: 2014
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-013-0499-x 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:162:y:2014:i:3:d:10.1007_s10957-013-0499-x

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

DOI: 10.1007/s10957-013-0499-x

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 ().