Minimizing quadratic functions subject to bound constraints with the rate oconvergence and finite termination

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F05%3A00012364" target="_blank" >RIV/61989100:27240/05:00012364 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Minimizing quadratic functions subject to bound constraints with the rate oconvergence and finite termination

Popis výsledku v původním jazyce

A new active set based algorithm is proposed that uses the conjugate gradient method to explore the face of the feasible region defined by the current iterate and the reduced gradient projection with the fixed steplength to expand the active set. The precision of approximate solutions of the auxiliary unconstrained problems is controlled by the norm of violation of the Karush-Kuhn-Tucker conditions at active constraints and the scalar product of the reduced gradient with the reduced gradient projection.The modifications were exploited to find the rate of convergence in terms of the spectral condition number of the Hessian matrix, to prove its finite termination property even for problems whose solution does not satisfy the strict complementarity condition, and to avoid any backtracking at the cost of evaluation of an upper bound for the spectral radius of the Hessian matrix. The performance of the algorithm is illustrated on solution of the inner obstacle problems. The result is an im

Název v anglickém jazyce

Minimizing quadratic functions subject to bound constraints with the rate oconvergence and finite termination

Popis výsledku anglicky

A new active set based algorithm is proposed that uses the conjugate gradient method to explore the face of the feasible region defined by the current iterate and the reduced gradient projection with the fixed steplength to expand the active set. The precision of approximate solutions of the auxiliary unconstrained problems is controlled by the norm of violation of the Karush-Kuhn-Tucker conditions at active constraints and the scalar product of the reduced gradient with the reduced gradient projection.The modifications were exploited to find the rate of convergence in terms of the spectral condition number of the Hessian matrix, to prove its finite termination property even for problems whose solution does not satisfy the strict complementarity condition, and to avoid any backtracking at the cost of evaluation of an upper bound for the spectral radius of the Hessian matrix. The performance of the algorithm is illustrated on solution of the inner obstacle problems. The result is an im

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

<a href="/cs/project/ME%20641" target="_blank" >ME 641: Vývoj škálovatelných řešičů pro řešení kontaktních problémů elasticity a tvarovou optimalizaci</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2005

Kód důvěrnosti údajů

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

Název periodika

Computational Optimization and Applications

ISSN

09266003

e-ISSN

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Svazek periodika

30

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

12

Strana od-do

33-44

Kód UT WoS článku

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EID výsledku v databázi Scopus

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