Properties of the block BFGS update and its application to the limited-memory block BNS method for unconstrained minimization

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F19%3A00488869" target="_blank" >RIV/67985807:_____/19:00488869 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/46747885:24220/19:00009688

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s11075-018-0513-3" target="_blank" >http://dx.doi.org/10.1007/s11075-018-0513-3</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11075-018-0513-3" target="_blank" >10.1007/s11075-018-0513-3</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Properties of the block BFGS update and its application to the limited-memory block BNS method for unconstrained minimization

Popis výsledku v původním jazyce

A block version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) variable metric update formula and its modifications are investigated. In spite of the fact that this formula satisfies the quasi-Newton conditions with all used difference vectors and that the improvement of convergence is the best one in some sense for quadratic objective functions, for general functions, it does not guarantee that the corresponding direction vectors are descent directions. To overcome this difficulty, but at the same time utilize the advantageous properties of the block BFGS update, a block version of the limited-memory variable metric BNS method for large-scale unconstrained optimization is proposed. The global convergence of the algorithm is established for convex sufficiently smooth functions. Numerical experiments demonstrate the efficiency of the new method.

Název v anglickém jazyce

Properties of the block BFGS update and its application to the limited-memory block BNS method for unconstrained minimization

Popis výsledku anglicky

A block version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) variable metric update formula and its modifications are investigated. In spite of the fact that this formula satisfies the quasi-Newton conditions with all used difference vectors and that the improvement of convergence is the best one in some sense for quadratic objective functions, for general functions, it does not guarantee that the corresponding direction vectors are descent directions. To overcome this difficulty, but at the same time utilize the advantageous properties of the block BFGS update, a block version of the limited-memory variable metric BNS method for large-scale unconstrained optimization is proposed. The global convergence of the algorithm is established for convex 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

<a href="/cs/project/GA13-06684S" target="_blank" >GA13-06684S: Iterační metody ve výpočetní matematice: Analýza, předpodmínění a aplikace</a><br>

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

Numerical Algorithms

ISSN

1017-1398

e-ISSN

—

Svazek periodika

80

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

31

Strana od-do

957-987

Kód UT WoS článku

000461382900012

EID výsledku v databázi Scopus

2-s2.0-85044777886