KFU. Card publication. Uzawa-type iterative solution methods for constrained saddle point problems

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FEDERAL UNIVERSITY

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UZAWA-TYPE ITERATIVE SOLUTION METHODS FOR CONSTRAINED SADDLE POINT PROBLEMS

Form of presentation

Articles in international journals and collections

Year of publication

2019

Язык

русский

Authors, employees of KFU

Lapin Aleksandr Vasilevich, author

Bibliographic description in the original language

Lapin A. Uzawa-type iterative solution methods for constrained saddle point problems//Lobachevskii Journal of Mathematics. - 2018. - V.39, No.5. - P. 681-697.

Annotation

For finite-dimensional saddle point problem with a nonlinear monotone operator and constraints on direct variables, iterative methods are developed, which in the potential case can be viewed as preconditioned Uzawa methods or as Uzawa-block relaxation methods. Convergence conditions of the iterative methods are formulated in the form of operator inequalities connecting the operator of the problem and the preconditioning matrix. When applied to mesh problems, this allows us to construct suitable preconditioners that ensure the convergence and effective implementation of iterative methods and to obtain the admissible intervals of iterative parameters which don't depend on mesh parameters. The presented results are based on the general theory developed by the author with co-authors in recent years.

Keywords

Constrained saddle point problems mesh methods variational inequalities optimal control problems state and control constraints

The name of the journal

Lobachevskii Journal of Mathematics

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=195138&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Lapin Aleksandr Vasilevich	ru_RU
dc.date.accessioned	2019-01-01T00:00:00Z	ru_RU
dc.date.available	2019-01-01T00:00:00Z	ru_RU
dc.date.issued	2019	ru_RU
dc.identifier.citation	Lapin A. Uzawa-type iterative solution methods for constrained saddle point problems//Lobachevskii Journal of Mathematics. - 2018. - V.39, No.5. - P. 681-697.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=195138&p_lang=2	ru_RU
dc.description.abstract	Lobachevskii Journal of Mathematics	ru_RU
dc.description.abstract	For finite-dimensional saddle point problem with a nonlinear monotone operator and constraints on direct variables, iterative methods are developed, which in the potential case can be viewed as preconditioned Uzawa methods or as Uzawa-block relaxation methods. Convergence conditions of the iterative methods are formulated in the form of operator inequalities connecting the operator of the problem and the preconditioning matrix. When applied to mesh problems, this allows us to construct suitable preconditioners that ensure the convergence and effective implementation of iterative methods and to obtain the admissible intervals of iterative parameters which don't depend on mesh parameters. The presented results are based on the general theory developed by the author with co-authors in recent years.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject		ru_RU
dc.title	Uzawa-type iterative solution methods for constrained saddle point problems	ru_RU
dc.type	Articles in international journals and collections	ru_RU