New Variant of the Semi-Monotonic Augmented Lagrangian Algorithm

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68145535%3A_____%2F24%3A00598050" target="_blank" >RIV/68145535:_____/24:00598050 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.ctresources.info/ccc/download/ccc.10066.pdf" target="_blank" >https://www.ctresources.info/ccc/download/ccc.10066.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4203/ccc.8.5.1" target="_blank" >10.4203/ccc.8.5.1</a>

Jazyk výsledku

angličtina

Název v původním jazyce

New Variant of the Semi-Monotonic Augmented Lagrangian Algorithm

Popis výsledku v původním jazyce

SMALE is an efficient algorithm for solving quadratic programming problems with simple bounds and linear equality constraints. There are two variants of this method: one updates the parameter for precision control of an inner solver by a factor less than one (the preferable variant, as it does not change the Hessian via penalty update), and the other updates the penalty by a factor greater than one (resulting in a lower number of outer iterations and fewer Hessian multiplications in the inner solver). We use the MPRGP algorithm as an inner solver for solving bound-constrained quadratic programming problems. We introduce a new theoretically supported variant that updates both these parameters: multiplying the penalty by a factor greater than one and multiplying the parameter for precision control for the MPRGP stopping criterion by the square root of this factor. The larger penalty accelerates the outer loop, while the larger parameter for precision control accelerates the inner solver. Numerical experiments with the Total-FETI method demonstrate the effectiveness of this new variant.

Název v anglickém jazyce

New Variant of the Semi-Monotonic Augmented Lagrangian Algorithm

Popis výsledku anglicky

SMALE is an efficient algorithm for solving quadratic programming problems with simple bounds and linear equality constraints. There are two variants of this method: one updates the parameter for precision control of an inner solver by a factor less than one (the preferable variant, as it does not change the Hessian via penalty update), and the other updates the penalty by a factor greater than one (resulting in a lower number of outer iterations and fewer Hessian multiplications in the inner solver). We use the MPRGP algorithm as an inner solver for solving bound-constrained quadratic programming problems. We introduce a new theoretically supported variant that updates both these parameters: multiplying the penalty by a factor greater than one and multiplying the parameter for precision control for the MPRGP stopping criterion by the square root of this factor. The larger penalty accelerates the outer loop, while the larger parameter for precision control accelerates the inner solver. Numerical experiments with the Total-FETI method demonstrate the effectiveness of this new variant.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10102 - Applied mathematics

Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název statě ve sborníku

Proceedings of the Twelfth International Conference on Engineering Computational Technology

ISBN

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ISSN

2753-3239

e-ISSN

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Počet stran výsledku

9

Strana od-do

5.1

Název nakladatele

Civil-Comp Press

Místo vydání

Edinburgh

Místo konání akce

Praha

Datum konání akce

4. 9. 2024

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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