Application of the Infinitely Many Times Repeated BNS Update and Conjugate Directions to Limited-Memory Optimization Methods

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F19%3A00504548" target="_blank" >RIV/67985807:_____/19:00504548 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.21136/panm.2018.19" target="_blank" >http://dx.doi.org/10.21136/panm.2018.19</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.21136/panm.2018.19" target="_blank" >10.21136/panm.2018.19</a>

Result language
angličtina
Original language name
Application of the Infinitely Many Times Repeated BNS Update and Conjugate Directions to Limited-Memory Optimization Methods
Original language description
To improve the performance of the L-BFGS method for large scale unconstrained optimization, repeating of some BFGS updates was proposed. Since this can be time consuming, the extra updates need to be selected carefully. We show that groups of these updates can be repeated infinitely many times under some conditions, without a noticeable increase of the computational time. The limit update is a block BFGS update. It can be obtained by solving of some Lyapunov matrix equation whose order can be decreased by application of vector corrections for conjugacy. Global convergence of the proposed algorithm is established for convex and sufficiently smooth functions. Numerical results indicate the efficiency of the new method.
Czech name
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Czech description
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Programs and Algorithms of Numerical Mathematics 19
ISBN
978-80-85823-69-1
ISSN
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e-ISSN
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Number of pages
9
Pages from-to
177-185
Publisher name
Institute of Mathematics of the Czech Academy of Sciences
Place of publication
Prague
Event location
Hejnice
Event date
Jun 24, 2018
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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