Generalizations of the limited-memory BFGS method based on the quasi-product form of update
Result description
Two families of limited-memory variable metric or quasi-Newton methods for unconstrained minimization based on quasi-product form of update are derived. As for the first family, four variants how to utilize the Strang recurrences for the Broyden class ofvariable metric updates are investigated; three of them use the same number of stored vectors as the limited- memory BFGS method. Moreover, one of the variants does not require any additional matrix by vector multiplication. The second family uses vectors from the preceding iteration to construct a new class of variable metric updates. Resulting methods again require neither any additional matrix by vector multiplication nor any additional stored vector. Global convergence of four of presented methodsis established for convex sufficiently smooth functions. Numerical results indicate that two of the new methods can save computational time substantially for certain problems.
Keywords
unconstrained minimizationvariable metric methodslimited-memory methodsBroyden class updatesglobal convergencenumerical results
The result's identifiers
Result code in IS VaVaI
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Generalizations of the limited-memory BFGS method based on the quasi-product form of update
Original language description
Two families of limited-memory variable metric or quasi-Newton methods for unconstrained minimization based on quasi-product form of update are derived. As for the first family, four variants how to utilize the Strang recurrences for the Broyden class ofvariable metric updates are investigated; three of them use the same number of stored vectors as the limited- memory BFGS method. Moreover, one of the variants does not require any additional matrix by vector multiplication. The second family uses vectors from the preceding iteration to construct a new class of variable metric updates. Resulting methods again require neither any additional matrix by vector multiplication nor any additional stored vector. Global convergence of four of presented methodsis established for convex sufficiently smooth functions. Numerical results indicate that two of the new methods can save computational time substantially for certain problems.
Czech name
—
Czech description
—
Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—
Result continuities
Project
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Computational and Applied Mathematics
ISSN
0377-0427
e-ISSN
—
Volume of the periodical
241
Issue of the periodical within the volume
15 March
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
14
Pages from-to
116-129
UT code for WoS article
000312354100008
EID of the result in the Scopus database
—
Basic information
Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BA - General mathematics
Year of implementation
2013