A limited-memory optimization method using the infinitely many times repeated BNS update and conjugate directions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24220%2F19%3A00009689" target="_blank" >RIV/46747885:24220/19:00009689 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/67985807:_____/19:00497050

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0377042718306629" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0377042718306629</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>

Jazyk výsledku

angličtina

Název v původním jazyce

A limited-memory optimization method using the infinitely many times repeated BNS update and conjugate directions

Popis výsledku v původním jazyce

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 (Vlcek and Luksan, 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. Vlcek and Luksan (2015). Global convergence of the proposed algorithm is established for convex and sufficiently smooth functions. Numerical experiments demonstrate the efficiency of the new method.

Název v anglickém jazyce

A limited-memory optimization method using the infinitely many times repeated BNS update and conjugate directions

Popis výsledku anglicky

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 (Vlcek and Luksan, 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. Vlcek and Luksan (2015). Global convergence of the proposed algorithm is established for convex and sufficiently smooth functions. Numerical experiments demonstrate the efficiency of the new method.

Druh

J_imp - Článek v periodiku v databázi Web of Science

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 periodika

Journal of Computational and Applied Mathematics

ISSN

0377-0427

e-ISSN

—

Svazek periodika

351

Číslo periodika v rámci svazku

MAY

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

15

Strana od-do

14-28

Kód UT WoS článku

000468555100003

EID výsledku v databázi Scopus

2-s2.0-85057130621