KFU. Card publication. Constructing Mixed Algorithms on the Basis of Some Bundle Method

KAZAN
FEDERAL UNIVERSITY

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- 中文
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CONSTRUCTING MIXED ALGORITHMS ON THE BASIS OF SOME BUNDLE METHOD

Form of presentation

Articles in international journals and collections

Year of publication

2020

Язык

английский

Authors, employees of KFU

Yarullin Rashid Samatovich, author

Bibliographic description in the original language

Yarullin R., Constructing Mixed Algorithms on the Basis of Some Bundle Method//Communications in Computer and Information Science. - 2020. - Vol.1275 CCIS, Is.. - P.150-163.

Annotation

In the paper, a method is proposed for minimizing a nondifferentiable convex function. This method belongs to a class of bundle methods. In the developed method it is possible to periodically produce discarding all previously constructed cutting planes that form the model of the objective function. These discards are applied when approximation of the epigraph of the objective function is sufficiently good in the a neighborhood of the current iteration point, and the quality of this approximation is estimated by using the model of the objective function. It is proposed an approach for constructing mixed minimization algorithms on the basis of the developed bundle method with involving any relaxation methods. The opportunity to mix the developed bundle method with other methods is provided as follows. In the proposed method during discarding the cutting planes the main iteration points are fixed with the relaxation condition. Any relaxation minimization method can be used to build these points. Moreover, the convergence of all such mixed algorithms will be guaranteed by the convergence of the developed bundle method. It is important to note that the procedures for updating cutting planes introduced in the bundle method will be transferred to mixed algorithms. The convergence of the proposed method is investigated, its properties are discussed, an estimate of the accuracy of the solution and estimation of the complexity of finding an approximate solution are obtained.

Keywords

Nondifferentiable optimization, mixed algorithms, bundle methods, cutting planes, sequence of approximations, convex functions

The name of the journal

Communications in Computer and Information Science

URL

https://www.scopus.com/inward/record.uri?eid=2-s2.0-85092088401&doi=10.1007%2f978-3-030-58657-7_14&partnerID=40&md5=48522d8a8cb3a0f40cf2a9a6befeb129

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

https://repository.kpfu.ru/eng/?p_id=243226&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Yarullin Rashid Samatovich	ru_RU
dc.date.accessioned	2020-01-01T00:00:00Z	ru_RU
dc.date.available	2020-01-01T00:00:00Z	ru_RU
dc.date.issued	2020	ru_RU
dc.identifier.citation	Yarullin R., Constructing Mixed Algorithms on the Basis of Some Bundle Method//Communications in Computer and Information Science. - 2020. - Vol.1275 CCIS, Is.. - P.150-163.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=243226&p_lang=2	ru_RU
dc.description.abstract	Communications in Computer and Information Science	ru_RU
dc.description.abstract	In the paper, a method is proposed for minimizing a nondifferentiable convex function. This method belongs to a class of bundle methods. In the developed method it is possible to periodically produce discarding all previously constructed cutting planes that form the model of the objective function. These discards are applied when approximation of the epigraph of the objective function is sufficiently good in the a neighborhood of the current iteration point, and the quality of this approximation is estimated by using the model of the objective function. It is proposed an approach for constructing mixed minimization algorithms on the basis of the developed bundle method with involving any relaxation methods. The opportunity to mix the developed bundle method with other methods is provided as follows. In the proposed method during discarding the cutting planes the main iteration points are fixed with the relaxation condition. Any relaxation minimization method can be used to build these points. Moreover, the convergence of all such mixed algorithms will be guaranteed by the convergence of the developed bundle method. It is important to note that the procedures for updating cutting planes introduced in the bundle method will be transferred to mixed algorithms. The convergence of the proposed method is investigated, its properties are discussed, an estimate of the accuracy of the solution and estimation of the complexity of finding an approximate solution are obtained.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	Nondifferentiable optimization	ru_RU
dc.subject	mixed algorithms	ru_RU
dc.subject	bundle methods	ru_RU
dc.subject	cutting planes	ru_RU
dc.subject	sequence of approximations	ru_RU
dc.subject	convex functions	ru_RU
dc.title	Constructing Mixed Algorithms on the Basis of Some Bundle Method	ru_RU
dc.type	Articles in international journals and collections	ru_RU