Superrelaxation and the rate of convergence in minimizing quadratic functions subject to bound constraints

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F11%3A00021399" target="_blank" >RIV/61989100:27240/11:00021399 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/61989100:27240/11:86084112

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s10589-009-9237-6" target="_blank" >http://dx.doi.org/10.1007/s10589-009-9237-6</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10589-009-9237-6" target="_blank" >10.1007/s10589-009-9237-6</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Superrelaxation and the rate of convergence in minimizing quadratic functions subject to bound constraints

Popis výsledku v původním jazyce

The paper resolves the problem concerning the rate of convergence of the working set based MPRGP (modified proportioning with reduced gradient projection) algorithm with a long steplength of the reduced projected gradient step. The main results of this paper are the formula for the R-linear rate of convergence of MPRGP in terms of the spectral condition number of the Hessian matrix and the proof of the finite termination property for the problems whose solution does not satisfy the strict complementarity condition. The bound on the R-linear rate of convergence of the projected gradient is also included. For shorter steplengths these results were proved earlier by Dostal and Schoberl. The efficiency of the longer steplength is illustrated by numerical experiments. The result is an important ingredient in developing scalable algorithms for numerical solution of elliptic variational inequalities and substantiates the choice of parameters that turned out to be effective in numerical experi

Název v anglickém jazyce

Superrelaxation and the rate of convergence in minimizing quadratic functions subject to bound constraints

Popis výsledku anglicky

The paper resolves the problem concerning the rate of convergence of the working set based MPRGP (modified proportioning with reduced gradient projection) algorithm with a long steplength of the reduced projected gradient step. The main results of this paper are the formula for the R-linear rate of convergence of MPRGP in terms of the spectral condition number of the Hessian matrix and the proof of the finite termination property for the problems whose solution does not satisfy the strict complementarity condition. The bound on the R-linear rate of convergence of the projected gradient is also included. For shorter steplengths these results were proved earlier by Dostal and Schoberl. The efficiency of the longer steplength is illustrated by numerical experiments. The result is an important ingredient in developing scalable algorithms for numerical solution of elliptic variational inequalities and substantiates the choice of parameters that turned out to be effective in numerical experi

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2011

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

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Svazek periodika

48

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

22

Strana od-do

23-44

Kód UT WoS článku

000286717700002

EID výsledku v databázi Scopus

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