Properties of the block BFGS update and its application to the limited-memory block BNS method for unconstrained minimization
Result description
A block version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) variable metric update formula and its modifications are investigated. In spite of the fact that this formula satisfies the quasi-Newton conditions with all used difference vectors and that the improvement of convergence is the best one in some sense for quadratic objective functions, for general functions, it does not guarantee that the corresponding direction vectors are descent directions. To overcome this difficulty, but at the same time utilize the advantageous properties of the block BFGS update, a block version of the limited-memory variable metric BNS method for large-scale unconstrained optimization is proposed. The global convergence of the algorithm is established for convex sufficiently smooth functions. Numerical experiments demonstrate the efficiency of the new method.
Keywords
Unconstrained minimizationBlock variable metric methodsLimited-memory methodsBFGS updateGlobal convergenceNumerical results
The result's identifiers
Result code in IS VaVaI
Alternative codes found
RIV/46747885:24220/19:00009688
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Properties of the block BFGS update and its application to the limited-memory block BNS method for unconstrained minimization
Original language description
A block version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) variable metric update formula and its modifications are investigated. In spite of the fact that this formula satisfies the quasi-Newton conditions with all used difference vectors and that the improvement of convergence is the best one in some sense for quadratic objective functions, for general functions, it does not guarantee that the corresponding direction vectors are descent directions. To overcome this difficulty, but at the same time utilize the advantageous properties of the block BFGS update, a block version of the limited-memory variable metric BNS method for large-scale unconstrained optimization is proposed. The global convergence of the algorithm is established for convex sufficiently smooth functions. Numerical experiments demonstrate the efficiency of the new method.
Czech name
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Czech description
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Classification
Type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Numerical Algorithms
ISSN
1017-1398
e-ISSN
—
Volume of the periodical
80
Issue of the periodical within the volume
3
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
31
Pages from-to
957-987
UT code for WoS article
000461382900012
EID of the result in the Scopus database
2-s2.0-85044777886
Basic information
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Applied mathematics
Year of implementation
2019