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

Gradient-type Approaches to Inverse and Ill-Posed Problems of Mathematical Physics Full article

Journal

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

Output data

Year: 2024, Volume: 64, Number: 9, Pages: 1974-1990 Pages count : 17 DOI: 10.1134/s0965542524701136

Tags

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

Authors

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

Affiliations

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

Funding (1)

Russian Science Foundation

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

Submitted:	Apr 18, 2024
Accepted:	May 31, 2024
Published print:	Nov 7, 2024
Published online:	Nov 7, 2024

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

Пока нет цитирований