Two limited-memory optimization methods with minimum violation of the previous secant conditions
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F21%3A00545840" target="_blank" >RIV/67985807:_____/21:00545840 - isvavai.cz</a>
Alternative codes found
RIV/46747885:24220/21:00009642
Result on the web
<a href="http://dx.doi.org/10.1007/s10589-021-00318-y" target="_blank" >http://dx.doi.org/10.1007/s10589-021-00318-y</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10589-021-00318-y" target="_blank" >10.1007/s10589-021-00318-y</a>
Alternative languages
Result language
angličtina
Original language name
Two limited-memory optimization methods with minimum violation of the previous secant conditions
Original language description
Limited-memory variable metric methods based on the well-known Broyden-Fletcher-Goldfarb-Shanno (BFGS) update are widely used for large scale optimization. The block version of this update, derived for general objective functions in Vlček and Lukšan (Numerical Algorithms 2019), satisfies the secant conditions with all used difference vectors and for quadratic objective functions gives the best improvement of convergence in some sense, but the corresponding direction vectors are not descent directions generally. To guarantee the descent property of direction vectors and simultaneously violate the secant conditions as little as possible in some sense, two methods based on the block BFGS update are proposed. They can be advantageously used together with methods based on vector corrections for conjugacy. Here we combine two types of these corrections to satisfy the secant conditions with both the corrected and uncorrected (original) latest difference vectors. Global convergence of the proposed algorithm is established for convex and sufficiently smooth functions. Numerical experiments demonstrate the efficiency of the new methods.
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
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Computational Optimization and Applications
ISSN
0926-6003
e-ISSN
1573-2894
Volume of the periodical
80
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
26
Pages from-to
755-780
UT code for WoS article
000695105500001
EID of the result in the Scopus database
2-s2.0-85114824515