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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Programs and Algorithms of Numerical Mathematics 19

ISBN

978-80-85823-69-1

ISSN

—

e-ISSN

—

Počet stran výsledku

9

Strana od-do

177-185

Název nakladatele

Institute of Mathematics of the Czech Academy of Sciences

Místo vydání

Prague

Místo konání akce

Hejnice

Datum konání akce

24. 6. 2018

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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