On Optimality of the Parameters of Self-Scaling Memoryless Quasi-Newton Updating Formulae

Saman Babaie-Kafaki ()
Additional contact information
Saman Babaie-Kafaki: Institute for Research in Fundamental Sciences (IPM)

Journal of Optimization Theory and Applications, 2015, vol. 167, issue 1, No 5, 101 pages

Abstract: Abstract Based on eigenvalue analyses, well-structured upper bounds for the condition number of the scaled memoryless quasi-Newton updating formulae Broyden–Fletcher–Goldfarb–Shanno and Davidon–Fletcher–Powell are obtained. Then, it is shown that the scaling parameter proposed by Oren and Spedicato is the unique minimizer of the given upper bound for the condition number of scaled memoryless Broyden–Fletcher–Goldfarb–Shanno update, and the scaling parameter proposed by Oren and Luenberger is the unique minimizer of the given upper bound for the condition number of scaled memoryless Davidon–Fletcher–Powell update. Thus, scaling parameters proposed by Oren et al. may enhance numerical stability of the self-scaling memoryless Broyden–Fletcher–Goldfarb–Shanno and Davidon–Fletcher–Powell methods.

Keywords: Unconstrained optimization; Large-scale optimization; Memoryless quasi-Newton update; Eigenvalue; Condition number; 90C53; 49M37; 65F15 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-015-0724-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:167:y:2015:i:1:d:10.1007_s10957-015-0724-x

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

DOI: 10.1007/s10957-015-0724-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 ().