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Gradient-type Approaches to Inverse and Ill-Posed Problems of Mathematical Physics Научная публикация

Журнал

Computational Mathematics and Mathematical Physics
ISSN: 0965-5425 , E-ISSN: 1555-6662

Вых. Данные

Год: 2024, Том: 64, Номер: 9, Страницы: 1974-1990 Страниц : 17 DOI: 10.1134/s0965542524701136

Ключевые слова

inverse and ill-posed problems, inexact gradient, accelerated gradient methods, regularization, Richardson extrapolation, mathematical physics

Авторы

Akindinov G.D. ^1,2,3 , Gasnikov A.V. ^1,2,4 , Krivorotko O.I. ^1,3 , Matyukhin V.V. ¹ , Pletnev N.V. ¹

Организации

1	Moscow Institute of Physics and Technology
2	IITP RAS
3	Sobolev Institute of Mathematics
4	Innopolis University

Информация о финансировании (1)

Российский научный фонд

21-71-30005

In this paper we are trying to formalize the definition of gradient for inverse problems and other non-classical optimization problems such as gradient approaches to problems having to do with the calculus of variations. We provide the readers with several examples of converting the problem to the gradient-type problem, describe several properties of the obtained gradient problem, provide analysis on its convexity or smoothness, and proving the convergence of the algorithm.

Akindinov G.D. , Gasnikov A.V. , Krivorotko O.I. , Matyukhin V.V. , Pletnev N.V.
Gradient-type Approaches to Inverse and Ill-Posed Problems of Mathematical Physics
Computational Mathematics and Mathematical Physics. 2024. V.64. N9. P.1974-1990. DOI: 10.1134/s0965542524701136 WOS Scopus РИНЦ OpenAlex

Поступила в редакцию:	18 апр. 2024 г.
Принята к публикации:	31 мая 2024 г.
Опубликована в печати:	7 нояб. 2024 г.
Опубликована online:	7 нояб. 2024 г.

Web of science:	WOS:001351553000021
Scopus:	2-s2.0-85209594494
РИНЦ:	74529486
OpenAlex:	W4404125976

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