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 |
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| 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 |
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| Affiliations |
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Funding (1)
| 1 | Russian Science Foundation | 21-71-30005 |
Abstract:
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.
Cite:
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
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
Dates:
| Submitted: | Apr 18, 2024 |
| Accepted: | May 31, 2024 |
| Published print: | Nov 7, 2024 |
| Published online: | Nov 7, 2024 |
Identifiers:
| Web of science: | WOS:001351553000021 |
| Scopus: | 2-s2.0-85209594494 |
| Elibrary: | 74529486 |
| OpenAlex: | W4404125976 |