Flow Search Approach and New Bounds for the m-Step Linear Conjugate Gradient Algorithm

H. X. Huang, Z. A. Liang and P. M. Pardalos
Additional contact information
H. X. Huang: Tsinghua University
Z. A. Liang: Shanghai University of Finance and Economics
P. M. Pardalos: University of Florida

Journal of Optimization Theory and Applications, 2004, vol. 120, issue 1, No 3, 53-71

Abstract: Abstract A flow search approach is presented in this paper. In the approach, each iterative process involves a subproblem, whose variables are the stepsize parameters. Every feasible solution of the subproblem corresponds to some serial search stages, the stepsize parameters in different search stages may interact mutually, and their optimal values are determined by evaluating the total effect of the interaction. The main idea of the flow search approach is illustrated via the minimization of a convex quadratic function. Based on the flow search approach, some properties of the m-step linear conjugate gradient algorithm are analyzed and new bounds on its convergence rate are also presented. Theoretical and numerical results indicate that the new bounds are better than the well-known ones.

Keywords: Flow search approach; conjugate gradient algorithm; m-step linear conjugate gradient algorithm; convergence rate (search for similar items in EconPapers)
Date: 2004
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1023/B:JOTA.0000012732.62633.59 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:120:y:2004:i:1:d:10.1023_b:jota.0000012732.62633.59

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

DOI: 10.1023/B:JOTA.0000012732.62633.59

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 ().