A Limited-memory Optimization Method Using the Infinitely Many Times Repeated BNS Update and Conjugate Directions
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F19%3A00497050" target="_blank" >RIV/67985807:_____/19:00497050 - isvavai.cz</a>
Alternative codes found
RIV/46747885:24220/19:00009689
Result on the web
<a href="http://dx.doi.org/10.1016/j.cam.2018.10.054" target="_blank" >http://dx.doi.org/10.1016/j.cam.2018.10.054</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.cam.2018.10.054" target="_blank" >10.1016/j.cam.2018.10.054</a>
Alternative languages
Result language
angličtina
Original language name
A Limited-memory Optimization Method Using the Infinitely Many Times Repeated BNS Update and Conjugate Directions
Original language description
To improve the performance of the limited-memory variable metric L-BFGS method for large scale unconstrained optimization, repeating of some BFGS updates was proposed e.g. in Al-Baali (1999, 2002). Since the repeating process can be time consuming, the suitable extra updates need to be selected carefully. We show that for the limited-memory variable metric BNS method, matrix updating can be efficiently repeated infinitely many times under some conditions, with only a small increase of the number of arithmetic operations. The limit matrix can be written as a block BFGS update (Vlček and Lukšan, 2018), which can be obtained by solving of some low-order Lyapunov matrix equation. The resulting method can be advantageously combined with methods based on vector corrections for conjugacy, see e.g. Vlček and Lukšan (2015). Global convergence of the proposed algorithm is established for convex and 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
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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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
Journal of Computational and Applied Mathematics
ISSN
0377-0427
e-ISSN
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Volume of the periodical
351
Issue of the periodical within the volume
1 May
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
15
Pages from-to
14-28
UT code for WoS article
000468555100003
EID of the result in the Scopus database
2-s2.0-85057130621