Two limited-memory optimization methods with minimum violation of the previous secant conditions

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/46747885:24220/21:00009642

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Two limited-memory optimization methods with minimum violation of the previous secant conditions

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Two limited-memory optimization methods with minimum violation of the previous secant conditions

Popis výsledku anglicky

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.

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

2021

Kód důvěrnosti údajů

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

Název periodika

Computational Optimization and Applications

ISSN

0926-6003

e-ISSN

1573-2894

Svazek periodika

80

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

26

Strana od-do

755-780

Kód UT WoS článku

000695105500001

EID výsledku v databázi Scopus

2-s2.0-85114824515