KFU. Card publication. Splitting method with adaptive step-size

KAZAN
FEDERAL UNIVERSITY

- RUS
- 中文
- ES

SPLITTING METHOD WITH ADAPTIVE STEP-SIZE

Form of presentation

Articles in international journals and collections

Year of publication

2019

Язык

английский

Authors, employees of KFU

Konnov Igor Vasilevich, author

Pinyagina Olga Vladislavovna, author

Bibliographic description in the original language

Konnov I, Pinyagina O., Splitting method with adaptive step-size//Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). - 2019. - Vol.11548 LNCS, Is.. - P.46-58.

Annotation

We suggest the modified splitting method for mixed variational inequalities and prove its convergence under rather mild assumptions. This method maintains the basic convergence properties but does not require any iterative step-size search procedure. It involves a simple adaptive step-size choice, which takes into account the problem behavior along the iterative sequence. The key element of this approach is a given majorant step-size sequence converging to zero. The next decreased value of step-size is taken only when the current iterate does not give a sufficient descent of the objective function. This descent value is estimated with the help of an Armijo-type condition, similar to the rule used in the inexact step-size linesearch. If the current iterate gives a sufficient descent, we can even take an increasing step-size value at the next iterate. Preliminary results of computational experiments confirm the efficiency of the proposed modification in comparison with the ordinary splitting method using the inexact step-size linesearch procedure.

Keywords

Splitting method, Forward-backward method, Adaptive step-size choice, Mixed variational inequality, Nonsmooth optimization problem

The name of the journal

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

URL

https://www.scopus.com/inward/record.uri?eid=2-s2.0-85067660860&doi=10.1007%2f978-3-030-22629-9_4&partnerID=40&md5=2fb7c6f6e4e993cb01eebd54fd3330f2

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

https://repository.kpfu.ru/eng/?p_id=205938&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Konnov Igor Vasilevich	ru_RU
dc.contributor.author	Pinyagina Olga Vladislavovna	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	Konnov I, Pinyagina O., Splitting method with adaptive step-size//Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). - 2019. - Vol.11548 LNCS, Is.. - P.46-58.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=205938&p_lang=2	ru_RU
dc.description.abstract	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)	ru_RU
dc.description.abstract	We suggest the modified splitting method for mixed variational inequalities and prove its convergence under rather mild assumptions. This method maintains the basic convergence properties but does not require any iterative step-size search procedure. It involves a simple adaptive step-size choice, which takes into account the problem behavior along the iterative sequence. The key element of this approach is a given majorant step-size sequence converging to zero. The next decreased value of step-size is taken only when the current iterate does not give a sufficient descent of the objective function. This descent value is estimated with the help of an Armijo-type condition, similar to the rule used in the inexact step-size linesearch. If the current iterate gives a sufficient descent, we can even take an increasing step-size value at the next iterate. Preliminary results of computational experiments confirm the efficiency of the proposed modification in comparison with the ordinary splitting method using the inexact step-size linesearch procedure.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	Splitting method	ru_RU
dc.subject	Forward-backward method	ru_RU
dc.subject	Adaptive step-size choice	ru_RU
dc.subject	Mixed variational inequality	ru_RU
dc.subject	Nonsmooth optimization problem	ru_RU
dc.title	Splitting method with adaptive step-size	ru_RU
dc.type	Articles in international journals and collections	ru_RU